Unit Cubes 1 – Counting Faces

Consider the outside of cubes made out of 1×1×1 1 \times 1 \times 1 unit blocks, with side lengths n×n×n n \times n \times n , for n2 n \geq 2 , which we have painted red on the outside.

The following table shows the number of unit cubes which are colored on a given number of faces.

Cube Size3 faces red2 faces red1 face red
2×2×2 2 \times 2 \times 2 800
3×3×3 3 \times 3 \times 3 8126
4×4×44 \times 4 \times 4 ???

What is the sum of the numbers missing from the row for the 4×4×44 \times 4 \times 4 cube?

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