A wooden cube that is 20 cm on each side is composed of 1 cm x 1 cm x 1 cm cubes.

Q1: If you paint all 6 sides of the outside of the cube blue, how many cubes will have no blue paint?

With a 3 by 3 by 3 cube, there is just one cube in the middle that would have no paint.

With a 4 by 4 by 4 cube, there are 8 cubes in the center of the cube (2 x 2 x 2) with no paint.

With a 5 by 5 by 5 cube, there are 27 cubes in the center of the cube (3 x 3 x 3) with no paint.

Answer: The pattern continues so a 20 by 20 by 20 cube, there would be 18 x 18 x 18 (**5832**) cubes in the center of the cube with no paint.

Q2: What if the 20 x 20 x 20 cm cube is composed of 2 cm x 2 cm x 2 cm cubes?

Answer: There would now be 1000 cubes (10 x 10 x 10), there would be 8 x 8 x 8 (512) cubes in the center of the cue with no paint.