Take as first grid 9x the same 4x4 in 6x6 magic square and with the second fixed grid you get a magic 18x18 square consisting of 9 proportional 4x4 in 6x6 magic squares.
| 1x number from grid with 9x the same 4x4 in 6x6 magic square | |||||||||||||||||
| 1 | 6 | 9 | 34 | 32 | 29 | 1 | 6 | 9 | 34 | 32 | 29 | 1 | 6 | 9 | 34 | 32 | 29 | 
| 35 | 11 | 18 | 23 | 22 | 2 | 35 | 11 | 18 | 23 | 22 | 2 | 35 | 11 | 18 | 23 | 22 | 2 | 
| 33 | 25 | 20 | 13 | 16 | 4 | 33 | 25 | 20 | 13 | 16 | 4 | 33 | 25 | 20 | 13 | 16 | 4 | 
| 27 | 14 | 15 | 26 | 19 | 10 | 27 | 14 | 15 | 26 | 19 | 10 | 27 | 14 | 15 | 26 | 19 | 10 | 
| 7 | 24 | 21 | 12 | 17 | 30 | 7 | 24 | 21 | 12 | 17 | 30 | 7 | 24 | 21 | 12 | 17 | 30 | 
| 8 | 31 | 28 | 3 | 5 | 36 | 8 | 31 | 28 | 3 | 5 | 36 | 8 | 31 | 28 | 3 | 5 | 36 | 
| 1 | 6 | 9 | 34 | 32 | 29 | 1 | 6 | 9 | 34 | 32 | 29 | 1 | 6 | 9 | 34 | 32 | 29 | 
| 35 | 11 | 18 | 23 | 22 | 2 | 35 | 11 | 18 | 23 | 22 | 2 | 35 | 11 | 18 | 23 | 22 | 2 | 
| 33 | 25 | 20 | 13 | 16 | 4 | 33 | 25 | 20 | 13 | 16 | 4 | 33 | 25 | 20 | 13 | 16 | 4 | 
| 27 | 14 | 15 | 26 | 19 | 10 | 27 | 14 | 15 | 26 | 19 | 10 | 27 | 14 | 15 | 26 | 19 | 10 | 
| 7 | 24 | 21 | 12 | 17 | 30 | 7 | 24 | 21 | 12 | 17 | 30 | 7 | 24 | 21 | 12 | 17 | 30 | 
| 8 | 31 | 28 | 3 | 5 | 36 | 8 | 31 | 28 | 3 | 5 | 36 | 8 | 31 | 28 | 3 | 5 | 36 | 
| 1 | 6 | 9 | 34 | 32 | 29 | 1 | 6 | 9 | 34 | 32 | 29 | 1 | 6 | 9 | 34 | 32 | 29 | 
| 35 | 11 | 18 | 23 | 22 | 2 | 35 | 11 | 18 | 23 | 22 | 2 | 35 | 11 | 18 | 23 | 22 | 2 | 
| 33 | 25 | 20 | 13 | 16 | 4 | 33 | 25 | 20 | 13 | 16 | 4 | 33 | 25 | 20 | 13 | 16 | 4 | 
| 27 | 14 | 15 | 26 | 19 | 10 | 27 | 14 | 15 | 26 | 19 | 10 | 27 | 14 | 15 | 26 | 19 | 10 | 
| 7 | 24 | 21 | 12 | 17 | 30 | 7 | 24 | 21 | 12 | 17 | 30 | 7 | 24 | 21 | 12 | 17 | 30 | 
| 8 | 31 | 28 | 3 | 5 | 36 | 8 | 31 | 28 | 3 | 5 | 36 | 8 | 31 | 28 | 3 | 5 | 36 | 
| + 36x number from fixed grid | |||||||||||||||||
| 8 | 0 | 8 | 0 | 8 | 0 | 7 | 1 | 7 | 1 | 7 | 1 | 6 | 2 | 6 | 2 | 6 | 2 | 
| 0 | 8 | 0 | 8 | 0 | 8 | 1 | 7 | 1 | 7 | 1 | 7 | 2 | 6 | 2 | 6 | 2 | 6 | 
| 8 | 0 | 8 | 0 | 8 | 0 | 7 | 1 | 7 | 1 | 7 | 1 | 6 | 2 | 6 | 2 | 6 | 2 | 
| 0 | 0 | 8 | 0 | 8 | 8 | 1 | 1 | 7 | 1 | 7 | 7 | 2 | 2 | 6 | 2 | 6 | 6 | 
| 0 | 8 | 0 | 8 | 0 | 8 | 1 | 7 | 1 | 7 | 1 | 7 | 2 | 6 | 2 | 6 | 2 | 6 | 
| 8 | 8 | 0 | 8 | 0 | 0 | 7 | 7 | 1 | 7 | 1 | 1 | 6 | 6 | 2 | 6 | 2 | 2 | 
| 5 | 3 | 5 | 3 | 5 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 5 | 3 | 5 | 3 | 5 | 
| 3 | 5 | 3 | 5 | 3 | 5 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 3 | 5 | 3 | 5 | 3 | 
| 5 | 3 | 5 | 3 | 5 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 5 | 3 | 5 | 3 | 5 | 
| 3 | 3 | 5 | 3 | 5 | 5 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 3 | 5 | 3 | 3 | 
| 3 | 5 | 3 | 5 | 3 | 5 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 3 | 5 | 3 | 5 | 3 | 
| 5 | 5 | 3 | 5 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 3 | 5 | 3 | 5 | 5 | 
| 2 | 6 | 2 | 6 | 2 | 6 | 1 | 7 | 1 | 7 | 1 | 7 | 0 | 8 | 0 | 8 | 0 | 8 | 
| 6 | 2 | 6 | 2 | 6 | 2 | 7 | 1 | 7 | 1 | 7 | 1 | 8 | 0 | 8 | 0 | 8 | 0 | 
| 2 | 6 | 2 | 6 | 2 | 6 | 1 | 7 | 1 | 7 | 1 | 7 | 0 | 8 | 0 | 8 | 0 | 8 | 
| 6 | 6 | 2 | 6 | 2 | 2 | 7 | 7 | 1 | 7 | 1 | 1 | 8 | 8 | 0 | 8 | 0 | 0 | 
| 6 | 2 | 6 | 2 | 6 | 2 | 7 | 1 | 7 | 1 | 7 | 1 | 8 | 0 | 8 | 0 | 8 | 0 | 
| 2 | 2 | 6 | 2 | 6 | 6 | 1 | 1 | 7 | 1 | 7 | 7 | 0 | 0 | 8 | 0 | 8 | 8 | 
| = 18x18 magic square consisting of 9x proportional 4x4 in 6x6 | |||||||||||||||||
| 289 | 6 | 297 | 34 | 320 | 29 | 253 | 42 | 261 | 70 | 284 | 65 | 217 | 78 | 225 | 106 | 248 | 101 | 
| 35 | 299 | 18 | 311 | 22 | 290 | 71 | 263 | 54 | 275 | 58 | 254 | 107 | 227 | 90 | 239 | 94 | 218 | 
| 321 | 25 | 308 | 13 | 304 | 4 | 285 | 61 | 272 | 49 | 268 | 40 | 249 | 97 | 236 | 85 | 232 | 76 | 
| 27 | 14 | 303 | 26 | 307 | 298 | 63 | 50 | 267 | 62 | 271 | 262 | 99 | 86 | 231 | 98 | 235 | 226 | 
| 7 | 312 | 21 | 300 | 17 | 318 | 43 | 276 | 57 | 264 | 53 | 282 | 79 | 240 | 93 | 228 | 89 | 246 | 
| 296 | 319 | 28 | 291 | 5 | 36 | 260 | 283 | 64 | 255 | 41 | 72 | 224 | 247 | 100 | 219 | 77 | 108 | 
| 181 | 114 | 189 | 142 | 212 | 137 | 145 | 150 | 153 | 178 | 176 | 173 | 109 | 186 | 117 | 214 | 140 | 209 | 
| 143 | 191 | 126 | 203 | 130 | 182 | 179 | 155 | 162 | 167 | 166 | 146 | 215 | 119 | 198 | 131 | 202 | 110 | 
| 213 | 133 | 200 | 121 | 196 | 112 | 177 | 169 | 164 | 157 | 160 | 148 | 141 | 205 | 128 | 193 | 124 | 184 | 
| 135 | 122 | 195 | 134 | 199 | 190 | 171 | 158 | 159 | 170 | 163 | 154 | 207 | 194 | 123 | 206 | 127 | 118 | 
| 115 | 204 | 129 | 192 | 125 | 210 | 151 | 168 | 165 | 156 | 161 | 174 | 187 | 132 | 201 | 120 | 197 | 138 | 
| 188 | 211 | 136 | 183 | 113 | 144 | 152 | 175 | 172 | 147 | 149 | 180 | 116 | 139 | 208 | 111 | 185 | 216 | 
| 73 | 222 | 81 | 250 | 104 | 245 | 37 | 258 | 45 | 286 | 68 | 281 | 1 | 294 | 9 | 322 | 32 | 317 | 
| 251 | 83 | 234 | 95 | 238 | 74 | 287 | 47 | 270 | 59 | 274 | 38 | 323 | 11 | 306 | 23 | 310 | 2 | 
| 105 | 241 | 92 | 229 | 88 | 220 | 69 | 277 | 56 | 265 | 52 | 256 | 33 | 313 | 20 | 301 | 16 | 292 | 
| 243 | 230 | 87 | 242 | 91 | 82 | 279 | 266 | 51 | 278 | 55 | 46 | 315 | 302 | 15 | 314 | 19 | 10 | 
| 223 | 96 | 237 | 84 | 233 | 102 | 259 | 60 | 273 | 48 | 269 | 66 | 295 | 24 | 309 | 12 | 305 | 30 | 
| 80 | 103 | 244 | 75 | 221 | 252 | 44 | 67 | 280 | 39 | 257 | 288 | 8 | 31 | 316 | 3 | 293 | 324 | 
    Notify that in the magic 18x18 square each 1/3 row/column/diagonal gives 1/3 of the magic sum.
     
I have used method composite, proportional (2) to construct
12x12, 18x18, 24x24, 30x30a and 30x30b