To construct a concentric magic square you can put each time a new border around the square to make it larger and larger and so you can construct a 4x4 in 6x6 in 8x8 in 10x10 in ... magic square.
1 | 8 | 13 | 12 | ||||||||||||
15 | 10 | 3 | 6 | ||||||||||||
4 | 5 | 16 | 9 | ||||||||||||
14 | 11 | 2 | 7 | ||||||||||||
1 | 6 | 9 | 34 | 32 | 29 | ||||||||||
35 | 11 | 18 | 23 | 22 | 2 | ||||||||||
33 | 25 | 20 | 13 | 16 | 4 | ||||||||||
27 | 14 | 15 | 26 | 19 | 10 | ||||||||||
7 | 24 | 21 | 12 | 17 | 30 | ||||||||||
8 | 31 | 28 | 3 | 5 | 36 | ||||||||||
57 | 12 | 52 | 14 | 1 | 3 | 63 | 58 | ||||||||
10 | 15 | 20 | 23 | 48 | 46 | 43 | 55 | ||||||||
9 | 49 | 25 | 32 | 37 | 36 | 16 | 56 | ||||||||
4 | 47 | 39 | 34 | 27 | 30 | 18 | 61 | ||||||||
54 | 41 | 28 | 29 | 40 | 33 | 24 | 11 | ||||||||
59 | 21 | 38 | 35 | 26 | 31 | 44 | 6 | ||||||||
60 | 22 | 45 | 42 | 17 | 19 | 50 | 5 | ||||||||
7 | 53 | 13 | 51 | 64 | 62 | 2 | 8 | ||||||||
92 | 2 | 98 | 4 | 14 | 18 | 84 | 16 | 86 | 91 | ||||||
88 | 75 | 30 | 70 | 32 | 19 | 21 | 81 | 76 | 13 | ||||||
12 | 28 | 33 | 38 | 41 | 66 | 64 | 61 | 73 | 89 | ||||||
90 | 27 | 67 | 43 | 50 | 55 | 54 | 34 | 74 | 11 | ||||||
5 | 22 | 65 | 57 | 52 | 45 | 48 | 36 | 79 | 96 | ||||||
100 | 72 | 59 | 46 | 47 | 58 | 51 | 42 | 29 | 1 | ||||||
8 | 77 | 39 | 56 | 53 | 44 | 49 | 62 | 24 | 93 | ||||||
94 | 78 | 40 | 63 | 60 | 35 | 37 | 68 | 23 | 7 | ||||||
6 | 25 | 71 | 31 | 69 | 82 | 80 | 20 | 26 | 95 | ||||||
10 | 99 | 3 | 97 | 87 | 83 | 17 | 85 | 15 | 9 | ||||||
134 | 143 | 3 | 141 | 5 | 1 | 22 | 124 | 20 | 126 | 18 | 133 | ||||
16 | 114 | 24 | 120 | 26 | 36 | 40 | 106 | 38 | 108 | 113 | 129 | ||||
15 | 110 | 97 | 52 | 92 | 54 | 41 | 43 | 103 | 98 | 35 | 130 | ||||
131 | 34 | 50 | 55 | 60 | 63 | 88 | 86 | 83 | 95 | 111 | 14 | ||||
132 | 112 | 49 | 89 | 65 | 72 | 77 | 76 | 56 | 96 | 33 | 13 | ||||
139 | 27 | 44 | 87 | 79 | 74 | 67 | 70 | 58 | 101 | 118 | 6 | ||||
128 | 122 | 94 | 81 | 68 | 69 | 80 | 73 | 64 | 51 | 23 | 17 | ||||
10 | 30 | 99 | 61 | 78 | 75 | 66 | 71 | 84 | 46 | 115 | 135 | ||||
9 | 116 | 100 | 62 | 85 | 82 | 57 | 59 | 90 | 45 | 29 | 136 | ||||
137 | 28 | 47 | 93 | 53 | 91 | 104 | 102 | 42 | 48 | 117 | 8 | ||||
7 | 32 | 121 | 25 | 119 | 109 | 105 | 39 | 107 | 37 | 31 | 138 | ||||
12 | 2 | 142 | 4 | 140 | 144 | 123 | 21 | 125 | 19 | 127 | 11 | ||||
13 | 189 | 9 | 187 | 11 | 185 | 1 | 190 | 15 | 181 | 17 | 179 | 19 | 183 | ||
21 | 160 | 169 | 29 | 167 | 31 | 27 | 48 | 150 | 46 | 152 | 44 | 159 | 176 | ||
175 | 42 | 140 | 50 | 146 | 52 | 62 | 66 | 132 | 64 | 134 | 139 | 155 | 22 | ||
23 | 41 | 136 | 123 | 78 | 118 | 80 | 67 | 69 | 129 | 124 | 61 | 156 | 174 | ||
173 | 157 | 60 | 76 | 81 | 86 | 89 | 114 | 112 | 109 | 121 | 137 | 40 | 24 | ||
25 | 158 | 138 | 75 | 115 | 91 | 98 | 103 | 102 | 82 | 122 | 59 | 39 | 172 | ||
171 | 165 | 53 | 70 | 113 | 105 | 100 | 93 | 96 | 84 | 127 | 144 | 32 | 26 | ||
177 | 154 | 148 | 120 | 107 | 94 | 95 | 106 | 99 | 90 | 77 | 49 | 43 | 20 | ||
191 | 36 | 56 | 125 | 87 | 104 | 101 | 92 | 97 | 110 | 72 | 141 | 161 | 6 | ||
5 | 35 | 142 | 126 | 88 | 111 | 108 | 83 | 85 | 116 | 71 | 55 | 162 | 192 | ||
193 | 163 | 54 | 73 | 119 | 79 | 117 | 130 | 128 | 68 | 74 | 143 | 34 | 4 | ||
3 | 33 | 58 | 147 | 51 | 145 | 135 | 131 | 65 | 133 | 63 | 57 | 164 | 194 | ||
195 | 38 | 28 | 168 | 30 | 166 | 170 | 149 | 47 | 151 | 45 | 153 | 37 | 2 | ||
14 | 8 | 188 | 10 | 186 | 12 | 196 | 7 | 182 | 16 | 180 | 18 | 178 | 184 | ||
15 | 248 | 10 | 246 | 12 | 244 | 243 | 23 | 8 | 17 | 18 | 238 | 237 | 21 | 235 | 241 |
233 | 43 | 219 | 39 | 217 | 41 | 215 | 31 | 220 | 45 | 211 | 47 | 209 | 49 | 213 | 24 |
25 | 51 | 190 | 199 | 59 | 197 | 61 | 57 | 78 | 180 | 76 | 182 | 74 | 189 | 206 | 232 |
231 | 205 | 72 | 170 | 80 | 176 | 82 | 92 | 96 | 162 | 94 | 164 | 169 | 185 | 52 | 26 |
27 | 53 | 71 | 166 | 153 | 108 | 148 | 110 | 97 | 99 | 159 | 154 | 91 | 186 | 204 | 230 |
229 | 203 | 187 | 90 | 106 | 111 | 116 | 119 | 144 | 142 | 139 | 151 | 167 | 70 | 54 | 28 |
29 | 55 | 188 | 168 | 105 | 145 | 121 | 128 | 133 | 132 | 112 | 152 | 89 | 69 | 202 | 228 |
227 | 201 | 195 | 83 | 100 | 143 | 135 | 130 | 123 | 126 | 114 | 157 | 174 | 62 | 56 | 30 |
256 | 207 | 184 | 178 | 150 | 137 | 124 | 125 | 136 | 129 | 120 | 107 | 79 | 73 | 50 | 1 |
250 | 221 | 66 | 86 | 155 | 117 | 134 | 131 | 122 | 127 | 140 | 102 | 171 | 191 | 36 | 7 |
6 | 35 | 65 | 172 | 156 | 118 | 141 | 138 | 113 | 115 | 146 | 101 | 85 | 192 | 222 | 251 |
252 | 223 | 193 | 84 | 103 | 149 | 109 | 147 | 160 | 158 | 98 | 104 | 173 | 64 | 34 | 5 |
4 | 33 | 63 | 88 | 177 | 81 | 175 | 165 | 161 | 95 | 163 | 93 | 87 | 194 | 224 | 253 |
254 | 225 | 68 | 58 | 198 | 60 | 196 | 200 | 179 | 77 | 181 | 75 | 183 | 67 | 32 | 3 |
2 | 44 | 38 | 218 | 40 | 216 | 42 | 226 | 37 | 212 | 46 | 210 | 48 | 208 | 214 | 255 |
16 | 9 | 247 | 11 | 245 | 13 | 14 | 234 | 249 | 240 | 239 | 19 | 20 | 236 | 22 | 242 |
Take the 14x14 concentric magic square, add 30 to all numbers and construct the border [see webpage 14x14 in 16x16 (1)]
See how the concentric magic square on this website is growing bigger and bigger:
3x3, 4x4, 5x5, 6x6, 7x7, 8x8, 9x9, 10x10, 11x11, 12x12, 13x13, 14x14, 15x15, 16x16, 17x1718x18, 19x19, 20x20, 21x21, 22x22, 23x23, 24x24, 25x25, 26x26, 27x27, 28x28, 29x29, 30x30, 31x31 and 32x32