Magic Constant of Magic Cube/Sequence

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Sequence of Magic Constants of Magic Cubes

The sequence of the magic constants of magic cubes of order $n$ begins:

$1, (9,) \, 42, 130, 315, 651, 1204, 2052, 3285, 5005, 7326, 10 \, 374, 14 \, 287, 19 \, 215, 25 \, 320, 32 \, 776, \ldots$

However, note that while $9 = \dfrac {2 \paren {2^3 + 1} } 2$, a magic cube of order $2$ does not actually exist.

This sequence is A027441 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).