Explanation about 6x6 magic square
The 6x6 magic square is double odd (2x3 = double prime number). Double prime number magic squares have an irregular structure. That's why there are no pure panmagic and/or compact and/or symmetric 6x6 magic squares. To get 6x6 magic squares you need to puzzle. For more detailed information about magic squares, see the explanation of the 3x3, 4x4 and 5x5 magic square.
N.B.: Prof. Hidetoshi Mino has counted the magic squares of order 6:
There are 17 753 889 189 701 384 304 different 6x6 magic squares.
The construction methods of the 6x6 magic square are:
Most perfect magic 6x6 square is a panmagic 4x4 in magic 6x6 square.