You have *n* cubical building blocks. You try to arrange them into the largest possible solid cube, but you find that don’t have quite enough blocks: One side of the large cube has exactly one row too few.

Prove that *n* is divisible by 6.

You have *n* cubical building blocks. You try to arrange them into the largest possible solid cube, but you find that don’t have quite enough blocks: One side of the large cube has exactly one row too few.

Prove that *n* is divisible by 6.