2D and 3D crosses

The idea here is to start with a square, then add a square to cover each exposed edge on every iteration.

Can you find a nice formula for the number of squares on the nth iteration? Can you find a nice formula for the difference between the number of squares on the nth iteration and the (n + 1)th?


The idea here is to start with a cube, then add a cube to cover each exposed face on every iteration.

Can you find a nice formula for the number of squares on the nth iteration? Can you find a nice formula for the difference between the number of squares on the nth iteration and the (n + 1)th?