# Unit Cubes 1 – Counting Faces

Consider the outside of cubes made out of $$1 \times 1 \times 1$$ unit blocks, with side lengths $$n \times n \times n$$, for $$n \geq 2$$, 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 Size 3 faces red 2 faces red 1 face red $$2 \times 2 \times 2$$ 8 0 0 $$3 \times 3 \times 3$$ 8 12 6 $$4 \times 4 \times 4$$ ? ? ?

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

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