A cube is painted red on all sides and is cut into 216 cubes of equal volume. How many cubes have exactly 2 sides painted red?

Question

A cube is painted red on all sides and is cut into 216 cubes of equal volume. How many cubes have exactly 2 sides painted red?

Answer 1

The cubes that have exactly two sides painted are those on the edge, yet not the corner - they have three sides painted.

On each edge there are 4 cubes that are not corners.

There are 8 edges. 

There are 32 (8 x 4) cubes with exactly two faces painted.

Answer 2

Since Volume = 216 cubes = 6³ cubles, so we have 6 cubes on each edge, and 6x6 = 36 cubes at each of the 6 faces

Since 2 faces are painted red, so number cubes painted red on 2 sides = 2*36=72 cubes