Use a pantriagonal 4x4x4 magic cube and a panmagic 7x7 square to construct a pantriagonal 28x28x28 magic cube, consisting of 343 proportional pantriagonal 4x4x4 magic cubes.

 

The first griod consists of 343x pantriagonal 4x4x4 magic cube. The second grids consists of the 7x7 panmagic square and its inverse. The third grid consists of the numbers 0 up to 6. Take 1x number from first grid + 64 x (number -/- 1) from second grid + 64x49x number from third grid. See the grids and the results of the first level below.

 

 

Take 1x number from first grid of 28x28x28 magic cube [level 1] 

6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43
51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30
16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33
57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24
6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43
51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30
16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33
57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24
6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43
51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30
16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33
57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24
6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43
51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30
16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33
57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24
6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43
51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30
16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33
57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24
6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43
51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30
16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33
57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24
6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43	6	27	54	43
51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30	51	46	3	30
16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33	16	17	64	33
57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24	57	40	9	24

 

 

 

+ 64x (number -/- 1) from second grid of 28x28x28 magic cube [level 1]

1	49	1	49	35	15	35	15	16	34	16	34	45	5	45	5	39	11	39	11	26	24	26	24	13	37	13	37
49	1	49	1	15	35	15	35	34	16	34	16	5	45	5	45	11	39	11	39	24	26	24	26	37	13	37	13
1	49	1	49	35	15	35	15	16	34	16	34	45	5	45	5	39	11	39	11	26	24	26	24	13	37	13	37
49	1	49	1	15	35	15	35	34	16	34	16	5	45	5	45	11	39	11	39	24	26	24	26	37	13	37	13
47	3	47	3	41	9	41	9	22	28	22	28	14	36	14	36	2	48	2	48	31	19	31	19	18	32	18	32
3	47	3	47	9	41	9	41	28	22	28	22	36	14	36	14	48	2	48	2	19	31	19	31	32	18	32	18
47	3	47	3	41	9	41	9	22	28	22	28	14	36	14	36	2	48	2	48	31	19	31	19	18	32	18	32
3	47	3	47	9	41	9	41	28	22	28	22	36	14	36	14	48	2	48	2	19	31	19	31	32	18	32	18
10	40	10	40	4	46	4	46	33	17	33	17	20	30	20	30	43	7	43	7	42	8	42	8	23	27	23	27
40	10	40	10	46	4	46	4	17	33	17	33	30	20	30	20	7	43	7	43	8	42	8	42	27	23	27	23
10	40	10	40	4	46	4	46	33	17	33	17	20	30	20	30	43	7	43	7	42	8	42	8	23	27	23	27
40	10	40	10	46	4	46	4	17	33	17	33	30	20	30	20	7	43	7	43	8	42	8	42	27	23	27	23
21	29	21	29	44	6	44	6	38	12	38	12	25	25	25	25	12	38	12	38	6	44	6	44	29	21	29	21
29	21	29	21	6	44	6	44	12	38	12	38	25	25	25	25	38	12	38	12	44	6	44	6	21	29	21	29
21	29	21	29	44	6	44	6	38	12	38	12	25	25	25	25	12	38	12	38	6	44	6	44	29	21	29	21
29	21	29	21	6	44	6	44	12	38	12	38	25	25	25	25	38	12	38	12	44	6	44	6	21	29	21	29
27	23	27	23	8	42	8	42	7	43	7	43	30	20	30	20	17	33	17	33	46	4	46	4	40	10	40	10
23	27	23	27	42	8	42	8	43	7	43	7	20	30	20	30	33	17	33	17	4	46	4	46	10	40	10	40
27	23	27	23	8	42	8	42	7	43	7	43	30	20	30	20	17	33	17	33	46	4	46	4	40	10	40	10
23	27	23	27	42	8	42	8	43	7	43	7	20	30	20	30	33	17	33	17	4	46	4	46	10	40	10	40
32	18	32	18	19	31	19	31	48	2	48	2	36	14	36	14	28	22	28	22	9	41	9	41	3	47	3	47
18	32	18	32	31	19	31	19	2	48	2	48	14	36	14	36	22	28	22	28	41	9	41	9	47	3	47	3
32	18	32	18	19	31	19	31	48	2	48	2	36	14	36	14	28	22	28	22	9	41	9	41	3	47	3	47
18	32	18	32	31	19	31	19	2	48	2	48	14	36	14	36	22	28	22	28	41	9	41	9	47	3	47	3
37	13	37	13	24	26	24	26	11	39	11	39	5	45	5	45	34	16	34	16	15	35	15	35	49	1	49	1
13	37	13	37	26	24	26	24	39	11	39	11	45	5	45	5	16	34	16	34	35	15	35	15	1	49	1	49
37	13	37	13	24	26	24	26	11	39	11	39	5	45	5	45	34	16	34	16	15	35	15	35	49	1	49	1
13	37	13	37	26	24	26	24	39	11	39	11	45	5	45	5	16	34	16	34	35	15	35	15	1	49	1	49

 

 

+ 64x49x number from third grid of 28x28x28 magic cube [level 1]

0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0
0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0
0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0
0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0
0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0
0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0
0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0
0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0
0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0
0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0
0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0
0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0
0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0
0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6
6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0	6	0

 

 

= 28x28x28 pantriagonal magic cube onsisting of 343x pantriagonal 4x4x4 cube

6	21915	54	21931	2182	19739	2230	19755	966	20955	1014	20971	2822	19099	2870	19115	2438	19483	2486	19499	1606	20315	1654	20331	774	21147	822	21163
21939	46	21891	30	19763	2222	19715	2206	20979	1006	20931	990	19123	2862	19075	2846	19507	2478	19459	2462	20339	1646	20291	1630	21171	814	21123	798
16	21905	64	21921	2192	19729	2240	19745	976	20945	1024	20961	2832	19089	2880	19105	2448	19473	2496	19489	1616	20305	1664	20321	784	21137	832	21153
21945	40	21897	24	19769	2216	19721	2200	20985	1000	20937	984	19129	2856	19081	2840	19513	2472	19465	2456	20345	1640	20297	1624	21177	808	21129	792
2950	18971	2998	18987	2566	19355	2614	19371	1350	20571	1398	20587	838	21083	886	21099	70	21851	118	21867	1926	19995	1974	20011	1094	20827	1142	20843
18995	2990	18947	2974	19379	2606	19331	2590	20595	1390	20547	1374	21107	878	21059	862	21875	110	21827	94	20019	1966	19971	1950	20851	1134	20803	1118
2960	18961	3008	18977	2576	19345	2624	19361	1360	20561	1408	20577	848	21073	896	21089	80	21841	128	21857	1936	19985	1984	20001	1104	20817	1152	20833
19001	2984	18953	2968	19385	2600	19337	2584	20601	1384	20553	1368	21113	872	21065	856	21881	104	21833	88	20025	1960	19977	1944	20857	1128	20809	1112
582	21339	630	21355	198	21723	246	21739	2054	19867	2102	19883	1222	20699	1270	20715	2694	19227	2742	19243	2630	19291	2678	19307	1414	20507	1462	20523
21363	622	21315	606	21747	238	21699	222	19891	2094	19843	2078	20723	1262	20675	1246	19251	2734	19203	2718	19315	2670	19267	2654	20531	1454	20483	1438
592	21329	640	21345	208	21713	256	21729	2064	19857	2112	19873	1232	20689	1280	20705	2704	19217	2752	19233	2640	19281	2688	19297	1424	20497	1472	20513
21369	616	21321	600	21753	232	21705	216	19897	2088	19849	2072	20729	1256	20681	1240	19257	2728	19209	2712	19321	2664	19273	2648	20537	1448	20489	1432
1286	20635	1334	20651	2758	19163	2806	19179	2374	19547	2422	19563	1542	20379	1590	20395	710	21211	758	21227	326	21595	374	21611	1798	20123	1846	20139
20659	1326	20611	1310	19187	2798	19139	2782	19571	2414	19523	2398	20403	1582	20355	1566	21235	750	21187	734	21619	366	21571	350	20147	1838	20099	1822
1296	20625	1344	20641	2768	19153	2816	19169	2384	19537	2432	19553	1552	20369	1600	20385	720	21201	768	21217	336	21585	384	21601	1808	20113	1856	20129
20665	1320	20617	1304	19193	2792	19145	2776	19577	2408	19529	2392	20409	1576	20361	1560	21241	744	21193	728	21625	360	21577	344	20153	1832	20105	1816
1670	20251	1718	20267	454	21467	502	21483	390	21531	438	21547	1862	20059	1910	20075	1030	20891	1078	20907	2886	19035	2934	19051	2502	19419	2550	19435
20275	1710	20227	1694	21491	494	21443	478	21555	430	21507	414	20083	1902	20035	1886	20915	1070	20867	1054	19059	2926	19011	2910	19443	2542	19395	2526
1680	20241	1728	20257	464	21457	512	21473	400	21521	448	21537	1872	20049	1920	20065	1040	20881	1088	20897	2896	19025	2944	19041	2512	19409	2560	19425
20281	1704	20233	1688	21497	488	21449	472	21561	424	21513	408	20089	1896	20041	1880	20921	1064	20873	1048	19065	2920	19017	2904	19449	2536	19401	2520
1990	19931	2038	19947	1158	20763	1206	20779	3014	18907	3062	18923	2246	19675	2294	19691	1734	20187	1782	20203	518	21403	566	21419	134	21787	182	21803
19955	2030	19907	2014	20787	1198	20739	1182	18931	3054	18883	3038	19699	2286	19651	2270	20211	1774	20163	1758	21427	558	21379	542	21811	174	21763	158
2000	19921	2048	19937	1168	20753	1216	20769	3024	18897	3072	18913	2256	19665	2304	19681	1744	20177	1792	20193	528	21393	576	21409	144	21777	192	21793
19961	2024	19913	2008	20793	1192	20745	1176	18937	3048	18889	3032	19705	2280	19657	2264	20217	1768	20169	1752	21433	552	21385	536	21817	168	21769	152
2310	19611	2358	19627	1478	20443	1526	20459	646	21275	694	21291	262	21659	310	21675	2118	19803	2166	19819	902	21019	950	21035	3078	18843	3126	18859
19635	2350	19587	2334	20467	1518	20419	1502	21299	686	21251	670	21683	302	21635	286	19827	2158	19779	2142	21043	942	20995	926	18867	3118	18819	3102
2320	19601	2368	19617	1488	20433	1536	20449	656	21265	704	21281	272	21649	320	21665	2128	19793	2176	19809	912	21009	960	21025	3088	18833	3136	18849
19641	2344	19593	2328	20473	1512	20425	1496	21305	680	21257	664	21689	296	21641	280	19833	2152	19785	2136	21049	936	21001	920	18873	3112	18825	3096

 

 

See for grids and result of 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)