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The class of diagonal magic cubes is the second of the six magic cube classes , coming after the simple magic cubes.
In a diagonal magic cube of order m, all 6m of the diagonals in the m planes parallel to the top, front, and sides of the cube must sum correctly. This means that the cube contains 3m simple magic squares of order m.Because the cube contains so many magic squares, it was considered for many years to be "perfect".
It is now known that there are three higher classes of cubes.
The diagonal magic cube has a total of 3m + 6m + 4 correctly summing lines and 3m + 6 simple magic squares.
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