Composite, Simple
It is possible to use one 3x3 magic square to produce a (simple) 9x9 magic square.
The first grid consists of 3x3 the same 3x3 magic square.
The second grid consists of the '3x3 blown up' version of the 3x3 magic square.
Take a number from a cell of the fist grid and add 9 x (number -/- 1) from the same cell of the second grid.
1x number
| 2 | 9 | 4 | 2 | 9 | 4 | 2 | 9 | 4 |
| 7 | 5 | 3 | 7 | 5 | 3 | 7 | 5 | 3 |
| 6 | 1 | 8 | 6 | 1 | 8 | 6 | 1 | 8 |
| 2 | 9 | 4 | 2 | 9 | 4 | 2 | 9 | 4 |
| 7 | 5 | 3 | 7 | 5 | 3 | 7 | 5 | 3 |
| 6 | 1 | 8 | 6 | 1 | 8 | 6 | 1 | 8 |
| 2 | 9 | 4 | 2 | 9 | 4 | 2 | 9 | 4 |
| 7 | 5 | 3 | 7 | 5 | 3 | 7 | 5 | 3 |
| 6 | 1 | 8 | 6 | 1 | 8 | 6 | 1 | 8 |
+ 9 x (number -/- 1)
| 2 | 2 | 2 | 9 | 9 | 9 | 4 | 4 | 4 |
| 2 | 2 | 2 | 9 | 9 | 9 | 4 | 4 | 4 |
| 2 | 2 | 2 | 9 | 9 | 9 | 4 | 4 | 4 |
| 7 | 7 | 7 | 5 | 5 | 5 | 3 | 3 | 3 |
| 7 | 7 | 7 | 5 | 5 | 5 | 3 | 3 | 3 |
| 7 | 7 | 7 | 5 | 5 | 5 | 3 | 3 | 3 |
| 6 | 6 | 6 | 1 | 1 | 1 | 8 | 8 | 8 |
| 6 | 6 | 6 | 1 | 1 | 1 | 8 | 8 | 8 |
| 6 | 6 | 6 | 1 | 1 | 1 | 8 | 8 | 8 |
= (simple) 9x9 magic square
| 11 | 18 | 13 | 74 | 81 | 76 | 29 | 36 | 31 |
| 16 | 14 | 12 | 79 | 77 | 75 | 34 | 32 | 30 |
| 15 | 10 | 17 | 78 | 73 | 80 | 33 | 28 | 35 |
| 56 | 63 | 58 | 38 | 45 | 40 | 20 | 27 | 22 |
| 61 | 59 | 57 | 43 | 41 | 39 | 25 | 23 | 21 |
| 60 | 55 | 62 | 42 | 37 | 44 | 24 | 19 | 26 |
| 47 | 54 | 49 | 2 | 9 | 4 | 65 | 72 | 67 |
| 52 | 50 | 48 | 7 | 5 | 3 | 70 | 68 | 66 |
| 51 | 46 | 53 | 6 | 1 | 8 | 69 | 64 | 71 |
Thanks to Mallesh K S, who pointed me that I was forgotten to present this method on my website. And he showed me that you can produce the following (not pure) 3x3 magic square by using the sum of the numbers of each 3x3 sub-square:
| 1107 | 1107 | 1107 | |||
| 1107 | 1107 | ||||
| 1107 | 126 | 693 | 288 | ||
| 1107 | 531 | 369 | 207 | ||
| 1107 | 450 | 45 | 612 |
I have used method composite, simple to construct 9x9, 12x12, 15x15a, 15x15b, 18x18, 20x20, 21x21a, 21x21b, 24x24a, 24x24b, 25x25, 27x27a, 27x27b, 28x28, 30x30a, 30x30b
