painted sides of a cube

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Painted Sides of a Cube

By Connor McInnes

Here is a 3 x 3 x 3 cube:

These 3 cubes all represent 3 x 3 x 3 cubes, the first one has the blocks shaded (pink) that will be painted 3 sides, the second cube has the blocks shaded (blue) that will have 2 sides painted, and the third cube has blocks shaded (green) that will have 1 side painted and all of the remaining cubes will have no sides painted.

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There is a definite pattern for the cube and the sides painted.
After looking at the first 4 cubes, the sides painted look as such:

 

In a 2 x 2 x 2 cube there are:
0 blocks with 0 sides painted.
0 blocks with 1 side painted.
0 blocks with 2 sides painted.
8 blocks with 3 sides painted.

In a 3 x 3 x 3 cube there are:
1 blocks with 0 sides painted.
6 blocks with 1 side painted.
12 blocks with 2 sides painted.
8 blocks with 3 sides painted.

In a 4 x 4 x 4 cube there are:
8 blocks with 0 sides ...

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