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**Robocop** Please explain the following formulae:

Each edge of a cube is equally divided into n parts, thus there are total n^{3} smaller cubes.

1) Let N_{0} be the number of smaller cubes with no exposed surfaces.

2) Let N_{1} be the number of smaller cubes with one exposed surfaces.

3) Let N_{2 }be the number of smaller cubes with two exposed surfaces.

For (1) i.e the number of smaller cubes with no exposed surface N_{0 }is given by the formula (n-2)^{3}. Why is 2 subtracted from n ? And why is (n-2) raised to the power 3 ?

For (2) i.e the number of smaller cubes with one exposed surfaces N_{1} is given by the formula 6(n-2)^{2} . Again why is 2 subtracted from n ? Why are we multiplying (n-2) with 6 ? And why is (n-2) raised to the power 2 and not 3 ?

For (3) i.e the number of smaller cubes with two exposed surfaces N_{2} is given by the formula 12(n-2). Again why are we multiplying (n-2) with 12 ? And why are we subtracting 2 from n ?

I will be very grateful if a detailed explanation is provided for the above formulae showing the dimensions clearly. For example Is 2 subtracted from n because it is the side layer or is there any other reason or is there any other way the cube is getting affected dimensionally? Thanks in advance!