Unit Cubes 1 – Counting Faces

Discrete Mathematics Level 2

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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