Use three grids to construct a diagonal 30x30x30 magic cube. The first grid consists of 125x diagonal 6x6x6 magic cube. The second grid consists of the 6x6 'blown up' 5x5 magic square (and half of it the inverse of the 5x5 magic square). The third grid consists of the numbers 0 up to 4, which are the row-/column coordinates of the 5x5 magic square. See below the grids and the result of level 1.

 

 

Take 1x number from first grid with 125x diagonal 6x6x6 [level 1]

109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112
87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126
140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82
75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138
136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86
104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107
109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112
87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126
140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82
75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138
136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86
104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107
109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112
87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126
140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82
75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138
136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86
104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107
109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112
87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126
140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82
75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138
136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86
104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107
109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112	109	143	76	123	88	112
87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126	87	156	49	170	63	126
140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82	140	174	52	150	53	82
75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138	75	66	182	51	139	138
136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86	136	40	148	65	176	86
104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107	104	72	144	92	132	107

 

 

+ 216x (number -/- 1) from second grid with the 6x6 'blown up' 5x5 [level 1]

1	1	1	1	1	1	15	15	15	15	15	15	22	22	22	22	22	22	18	18	18	18	18	18	9	9	9	9	9	9
1	1	1	1	1	1	15	15	15	15	15	15	22	22	22	22	22	22	18	18	18	18	18	18	9	9	9	9	9	9
1	1	1	1	1	1	15	15	15	15	15	15	22	22	22	22	22	22	18	18	18	18	18	18	9	9	9	9	9	9
1	1	1	1	1	1	15	15	15	15	15	15	22	22	22	22	22	22	18	18	18	18	18	18	9	9	9	9	9	9
1	1	1	1	1	1	15	15	15	15	15	15	22	22	22	22	22	22	18	18	18	18	18	18	9	9	9	9	9	9
1	1	1	1	1	1	15	15	15	15	15	15	22	22	22	22	22	22	18	18	18	18	18	18	9	9	9	9	9	9
23	23	23	23	23	23	19	19	19	19	19	19	6	6	6	6	6	6	5	5	5	5	5	5	12	12	12	12	12	12
23	23	23	23	23	23	19	19	19	19	19	19	6	6	6	6	6	6	5	5	5	5	5	5	12	12	12	12	12	12
23	23	23	23	23	23	19	19	19	19	19	19	6	6	6	6	6	6	5	5	5	5	5	5	12	12	12	12	12	12
23	23	23	23	23	23	19	19	19	19	19	19	6	6	6	6	6	6	5	5	5	5	5	5	12	12	12	12	12	12
23	23	23	23	23	23	19	19	19	19	19	19	6	6	6	6	6	6	5	5	5	5	5	5	12	12	12	12	12	12
23	23	23	23	23	23	19	19	19	19	19	19	6	6	6	6	6	6	5	5	5	5	5	5	12	12	12	12	12	12
10	10	10	10	10	10	2	2	2	2	2	2	13	13	13	13	13	13	24	24	24	24	24	24	16	16	16	16	16	16
10	10	10	10	10	10	2	2	2	2	2	2	13	13	13	13	13	13	24	24	24	24	24	24	16	16	16	16	16	16
10	10	10	10	10	10	2	2	2	2	2	2	13	13	13	13	13	13	24	24	24	24	24	24	16	16	16	16	16	16
10	10	10	10	10	10	2	2	2	2	2	2	13	13	13	13	13	13	24	24	24	24	24	24	16	16	16	16	16	16
10	10	10	10	10	10	2	2	2	2	2	2	13	13	13	13	13	13	24	24	24	24	24	24	16	16	16	16	16	16
10	10	10	10	10	10	2	2	2	2	2	2	13	13	13	13	13	13	24	24	24	24	24	24	16	16	16	16	16	16
14	14	14	14	14	14	21	21	21	21	21	21	20	20	20	20	20	20	7	7	7	7	7	7	3	3	3	3	3	3
14	14	14	14	14	14	21	21	21	21	21	21	20	20	20	20	20	20	7	7	7	7	7	7	3	3	3	3	3	3
14	14	14	14	14	14	21	21	21	21	21	21	20	20	20	20	20	20	7	7	7	7	7	7	3	3	3	3	3	3
14	14	14	14	14	14	21	21	21	21	21	21	20	20	20	20	20	20	7	7	7	7	7	7	3	3	3	3	3	3
14	14	14	14	14	14	21	21	21	21	21	21	20	20	20	20	20	20	7	7	7	7	7	7	3	3	3	3	3	3
14	14	14	14	14	14	21	21	21	21	21	21	20	20	20	20	20	20	7	7	7	7	7	7	3	3	3	3	3	3
17	17	17	17	17	17	8	8	8	8	8	8	4	4	4	4	4	4	11	11	11	11	11	11	25	25	25	25	25	25
17	17	17	17	17	17	8	8	8	8	8	8	4	4	4	4	4	4	11	11	11	11	11	11	25	25	25	25	25	25
17	17	17	17	17	17	8	8	8	8	8	8	4	4	4	4	4	4	11	11	11	11	11	11	25	25	25	25	25	25
17	17	17	17	17	17	8	8	8	8	8	8	4	4	4	4	4	4	11	11	11	11	11	11	25	25	25	25	25	25
17	17	17	17	17	17	8	8	8	8	8	8	4	4	4	4	4	4	11	11	11	11	11	11	25	25	25	25	25	25
17	17	17	17	17	17	8	8	8	8	8	8	4	4	4	4	4	4	11	11	11	11	11	11	25	25	25	25	25	25

 

 

+216x25x number from third grid with row-/column coordinates 5x5 [level 1]

0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4
0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4
0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4
0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4
0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4
0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4
2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1
2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1
2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1
2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1
2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1
2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1
4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3
4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3
4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3
4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3
4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3
4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3
1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0
1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0
1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0
1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0
1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0
1	1	1	1	1	1	2	2	2	2	2	2	3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0
3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2
3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2
3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2
3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2
3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2
3	3	3	3	3	3	4	4	4	4	4	4	0	0	0	0	0	0	1	1	1	1	1	1	2	2	2	2	2	2

 

 

30x30x30 diagonal magic cube

109	143	76	123	88	112	8533	8567	8500	8547	8512	8536	15445	15479	15412	15459	15424	15448	19981	20015	19948	19995	19960	19984	23437	23471	23404	23451	23416	23440
87	156	49	170	63	126	8511	8580	8473	8594	8487	8550	15423	15492	15385	15506	15399	15462	19959	20028	19921	20042	19935	19998	23415	23484	23377	23498	23391	23454
140	174	52	150	53	82	8564	8598	8476	8574	8477	8506	15476	15510	15388	15486	15389	15418	20012	20046	19924	20022	19925	19954	23468	23502	23380	23478	23381	23410
75	66	182	51	139	138	8499	8490	8606	8475	8563	8562	15411	15402	15518	15387	15475	15474	19947	19938	20054	19923	20011	20010	23403	23394	23510	23379	23467	23466
136	40	148	65	176	86	8560	8464	8572	8489	8600	8510	15472	15376	15484	15401	15512	15422	20008	19912	20020	19937	20048	19958	23464	23368	23476	23393	23504	23414
104	72	144	92	132	107	8528	8496	8568	8516	8556	8531	15440	15408	15480	15428	15468	15443	19976	19944	20016	19964	20004	19979	23432	23400	23472	23420	23460	23435
15661	15695	15628	15675	15640	15664	20197	20231	20164	20211	20176	20200	22789	22823	22756	22803	22768	22792	973	1007	940	987	952	976	7885	7919	7852	7899	7864	7888
15639	15708	15601	15722	15615	15678	20175	20244	20137	20258	20151	20214	22767	22836	22729	22850	22743	22806	951	1020	913	1034	927	990	7863	7932	7825	7946	7839	7902
15692	15726	15604	15702	15605	15634	20228	20262	20140	20238	20141	20170	22820	22854	22732	22830	22733	22762	1004	1038	916	1014	917	946	7916	7950	7828	7926	7829	7858
15627	15618	15734	15603	15691	15690	20163	20154	20270	20139	20227	20226	22755	22746	22862	22731	22819	22818	939	930	1046	915	1003	1002	7851	7842	7958	7827	7915	7914
15688	15592	15700	15617	15728	15638	20224	20128	20236	20153	20264	20174	22816	22720	22828	22745	22856	22766	1000	904	1012	929	1040	950	7912	7816	7924	7841	7952	7862
15656	15624	15696	15644	15684	15659	20192	20160	20232	20180	20220	20195	22784	22752	22824	22772	22812	22787	968	936	1008	956	996	971	7880	7848	7920	7868	7908	7883
23653	23687	23620	23667	23632	23656	325	359	292	339	304	328	8101	8135	8068	8115	8080	8104	15877	15911	15844	15891	15856	15880	19549	19583	19516	19563	19528	19552
23631	23700	23593	23714	23607	23670	303	372	265	386	279	342	8079	8148	8041	8162	8055	8118	15855	15924	15817	15938	15831	15894	19527	19596	19489	19610	19503	19566
23684	23718	23596	23694	23597	23626	356	390	268	366	269	298	8132	8166	8044	8142	8045	8074	15908	15942	15820	15918	15821	15850	19580	19614	19492	19590	19493	19522
23619	23610	23726	23595	23683	23682	291	282	398	267	355	354	8067	8058	8174	8043	8131	8130	15843	15834	15950	15819	15907	15906	19515	19506	19622	19491	19579	19578
23680	23584	23692	23609	23720	23630	352	256	364	281	392	302	8128	8032	8140	8057	8168	8078	15904	15808	15916	15833	15944	15854	19576	19480	19588	19505	19616	19526
23648	23616	23688	23636	23676	23651	320	288	360	308	348	323	8096	8064	8136	8084	8124	8099	15872	15840	15912	15860	15900	15875	19544	19512	19584	19532	19572	19547
8317	8351	8284	8331	8296	8320	15229	15263	15196	15243	15208	15232	20413	20447	20380	20427	20392	20416	23005	23039	22972	23019	22984	23008	541	575	508	555	520	544
8295	8364	8257	8378	8271	8334	15207	15276	15169	15290	15183	15246	20391	20460	20353	20474	20367	20430	22983	23052	22945	23066	22959	23022	519	588	481	602	495	558
8348	8382	8260	8358	8261	8290	15260	15294	15172	15270	15173	15202	20444	20478	20356	20454	20357	20386	23036	23070	22948	23046	22949	22978	572	606	484	582	485	514
8283	8274	8390	8259	8347	8346	15195	15186	15302	15171	15259	15258	20379	20370	20486	20355	20443	20442	22971	22962	23078	22947	23035	23034	507	498	614	483	571	570
8344	8248	8356	8273	8384	8294	15256	15160	15268	15185	15296	15206	20440	20344	20452	20369	20480	20390	23032	22936	23044	22961	23072	22982	568	472	580	497	608	518
8312	8280	8352	8300	8340	8315	15224	15192	15264	15212	15252	15227	20408	20376	20448	20396	20436	20411	23000	22968	23040	22988	23028	23003	536	504	576	524	564	539
19765	19799	19732	19779	19744	19768	23221	23255	23188	23235	23200	23224	757	791	724	771	736	760	7669	7703	7636	7683	7648	7672	16093	16127	16060	16107	16072	16096
19743	19812	19705	19826	19719	19782	23199	23268	23161	23282	23175	23238	735	804	697	818	711	774	7647	7716	7609	7730	7623	7686	16071	16140	16033	16154	16047	16110
19796	19830	19708	19806	19709	19738	23252	23286	23164	23262	23165	23194	788	822	700	798	701	730	7700	7734	7612	7710	7613	7642	16124	16158	16036	16134	16037	16066
19731	19722	19838	19707	19795	19794	23187	23178	23294	23163	23251	23250	723	714	830	699	787	786	7635	7626	7742	7611	7699	7698	16059	16050	16166	16035	16123	16122
19792	19696	19804	19721	19832	19742	23248	23152	23260	23177	23288	23198	784	688	796	713	824	734	7696	7600	7708	7625	7736	7646	16120	16024	16132	16049	16160	16070
19760	19728	19800	19748	19788	19763	23216	23184	23256	23204	23244	23219	752	720	792	740	780	755	7664	7632	7704	7652	7692	7667	16088	16056	16128	16076	16116	16091

 

 

The rows/columns/diagonals in each level give the magic sum and 1/5 pillars, 1/5 diagonals and 1/5 (main) triagonals give 1/5 of the magic sum.

 

See for all levels and check if all numbers are in the magic cube and addition of the numbers give the right magic sum, the download below.

 

With method composite 5 you use a magic cube of order A and a magic square of order B to construct a magic cube of order AxB. See on this website the construction of:

20x20x20 (pantriagonal), 24x24x24 (diagonal), 24x24x24 (pantriagonal),

28x28x28 (pantriagonal), 30x30x30, (diagonal) and 30x30x30 (pantriagonal)