Kilominx and Megaminx God's Number searches are already pretty tight, at 18-34 and 48-194 respectively in terms of their lower and upper bounds verified, but I couldn't find much on other same-shaped puzzles such as Gigaminx or Teraminx, so using the same method as ones used for calculating...
n³-(n³-2)
Let’s use an example of a 5x5:
5³=125
3³=27
125-27=98
There are 98 cubees in a 5x5.
Please let me know if there’s a simpler way of showing this.
This doesn’t work for 2x2 btw. Just... use common sense