The following bordered magic square was created by Michael Stifel in 1544. A closer examination shows that it is not only bordered, but nested bordered or multi-bordered. You can also remove the border of the inner magic square of order 5 and will get another magic square of order 3. So continuous removing of the borders will always create new magic squares.
12 | 49 | 47 | 45 | 9 | 11 | 2 |
46 | 20 | 37 | 35 | 19 | 14 | 4 |
44 | 34 | 24 | 29 | 22 | 16 | 6 |
7 | 17 | 23 | 25 | 27 | 33 | 43 |
8 | 18 | 28 | 21 | 26 | 32 | 42 |
10 | 36 | 13 | 15 | 31 | 30 | 40 |
48 | 1 | 3 | 5 | 41 | 39 | 38 |
20 | 37 | 35 | 19 | 14 |
34 | 24 | 29 | 22 | 16 |
17 | 23 | 25 | 27 | 33 |
18 | 28 | 21 | 26 | 32 |
36 | 13 | 15 | 31 | 30 |
24 | 29 | 22 |
23 | 25 | 27 |
28 | 21 | 26 |
Another wonderful example of multi-concentric magic squares of order 12 is given by Kraitchik, which he shows in his book Mathematical Recreations on page 167. Four borders can be removed and each new inner square is magic again.
1 | 142 | 141 | 140 | 139 | 138 | 129 | 11 | 10 | 9 | 8 | 2 |
12 | 23 | 120 | 119 | 118 | 117 | 112 | 29 | 31 | 32 | 24 | 133 |
15 | 39 | 41 | 102 | 101 | 100 | 99 | 47 | 48 | 42 | 106 | 130 |
18 | 36 | 49 | 55 | 88 | 87 | 86 | 63 | 56 | 96 | 109 | 127 |
19 | 40 | 52 | 83 | 65 | 72 | 74 | 79 | 62 | 93 | 105 | 126 |
22 | 30 | 54 | 84 | 76 | 77 | 67 | 70 | 61 | 91 | 115 | 123 |
132 | 110 | 95 | 60 | 71 | 66 | 80 | 73 | 85 | 50 | 35 | 13 |
131 | 107 | 94 | 64 | 78 | 75 | 69 | 68 | 81 | 51 | 38 | 14 |
128 | 111 | 92 | 89 | 57 | 58 | 59 | 82 | 90 | 53 | 34 | 17 |
125 | 108 | 103 | 43 | 44 | 45 | 46 | 98 | 97 | 104 | 37 | 20 |
124 | 121 | 25 | 26 | 27 | 28 | 33 | 116 | 114 | 113 | 122 | 21 |
143 | 3 | 4 | 5 | 6 | 7 | 16 | 134 | 135 | 136 | 137 | 144 |