Magic Constant of Magic Cube/Sequence

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.