This will be hard to visualize, but I'll try to explain.

Suppose that n

^{3}sugar cubes are stacked to form an n x n x n cube. ( cube is 6 cubes wide, 6 cubes length and 6 cubes in height ) The large cube is now painted yellow. depending on where the sugar cube is positioned in the large cube, it may have one or several of it's 6 faces painted yellow.( For example, if n=1, all 6 faces are painted.) For larger n, there are some sugar cubes with unpainted faces.Give expressions in the variable n, n>3, for the number of sugar cubes in the n x n x n cube with 0,1,2 or 3 painted faces, respectively. The expressions obtained , when added together, should give n

^{3}for all n larger then equal to 3.Why?

Use algebraic simplification to check your identity in the variable n.

## Comments

^{3}