132: Cubes

If you've ever played with a Rubic's Cube, you know it's possible to divide a cube into 27 smaller cubes. Eight and sixty-four is pretty obvious, too.

Can you show how to divide a cube into other numbers of sub-cubes, numbers that aren't perfect cubic numbers?

Like 15? or 20?

Possible to divide a cube into 1, 8, and 27 cubes. Show how to also divide a cube into 20 or 15 sub cubes. Any other nmbrs under 27?
— James Tanton (@jamestanton) May 11, 2014

Because you don't have enough awesome in your life, I present watermelon cubes.