If you have a 10x10x10 cube painted on the outside, how many 1x1x1 cubes have no paint?

If you have a 10x10x10 cube painted on the outside, how many 1x1x1 cubes have no paint?

Approach: Subtract the outer layers to find the inner core.

512. The inner core is an 8x8x8 cube. 8^3 = 512.

Follow-up: How many cubes have paint on exactly one face?

Key concepts: volume, dimensions.