Explanation 18x18 magic square
The 18x18 magic square is double odd (2x9). Double odd magic squares have an irregular structure. That's why a pure panmagic, symmetric and/or compact 18x18 magic square does not exist. But, 18=3x6 and you can composite the 18x18 magic square using the 3x3 and the 6x6 magic square. It is possible to construct a 18x18 magic square consisting of 3x3 proportional 6x6 magic squares. Each 1/3 row/column/diagonal gives 1/3 of the magic sum. Special 18x18 magic squares are the 18x18 inlaid magic (with 16x16 inlay) square and the 18x18 concentric magic square.
Methods to construct the 18x18 magic square are:
N.B.: A pure 18x18 magic square which is 2x2 or 3x3 compact is not possible. However, composite proportional (1) and composite proportional (2) give pure 18x18 magic squares which are 6x6 compact.