mathematics
posted by danielle on .
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 ycolumn (or number of small cubes with one face painted). They have only given me the 5x5x5 corresponding yvalue 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.

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*((n2)^2)