There are 6^3 unit cubes that are put together to form a 6 × 6 × 6 cube. It is then painted red on all sides. How many of the unit cubes have paint on them?
Every cube on the outside "shell" has red on them -- some painted red on one side, some on two sides, and some on three sides.
It is probably easier to calculate how many of the unit cubes have no paint on them,
This will be all the interior cubes, which form a 5 x 5 x 5 cube = 125 unit cubes.