Posted by **danielle** on Wednesday, February 4, 2009 at 7:34pm.

so i have this table of values demonstrating the size of a cube to the number of small cubes with one face painted. The table starts with an x value (or number of small cubes) at 3x3x3, and goes up to 8x8x8. I need to fill in the y-column (or number of small cubes with one face painted). They have only given me the 5x5x5 corresponding y-value which is 54 as well as the 7x7x7 corresponding y value which is 150. I need to find a formula of some sort to find the rest. i don't know how to do this.. please help me.

- mathematics -
**economyst**, Thursday, February 5, 2009 at 9:17am
Drawing a picture helps.

In a 3x3 side of a cube there is 1 interior square, all the rest are edge pieces. Since there are 6 sides to a cube y for a 3x3 = 6

In a 4x4 there are 4 interior squares.

In a 5x5 there are 9 interior squares.

In a 6x6 there are 16 interior squares.

Notice a pattern yet. The number of interior squares is a perfect square

So the formula is y = 6*((n-2)^2)

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