# Painted Cube Faces

Probability Level 3

Consider an $n \times n \times n$ cube $(n \geq 3)$ whose outer surface is painted blue. The unit cubes at the corners each have 3 blue faces, while the unit cubes in the center each have 0 blue faces.

For what value of $n$ will the number of unit cubes with 0 blue faces be twice the number of unit cubes with 1 blue face?

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