Sum of Terms of Magic Cube/Sequence

Sequence of Sums of Terms of Magic Cubes
The sequence of the sum totals of all the entries in magic cubes of order $n$ begins:
 * $1, \paren {36,} \, 378, 2080, 7875, 23 \, 436, 58 \, 996, 131 \, 328, \ldots$

However, note that while $36 = \dfrac {2^3 \paren {2^3 + 1} } 2$, a magic cube of order $2$ does not actually exist.