Given Data

1. A cube is painted on all six outer faces and divided into 6 x 6 x 6 equal cubes.

Question

How many small cubes have exactly one face painted?

Answer

96.

Solution

1. Cubes with one painted face lie inside the six large faces, away from edges.
2. Each face contains (6 - 2)^2 = 16 such cubes.
3. 6 x 16 = 96.