A cube of side 49 cm is painted purple on all the faces and then cut into smaller cubes of sides 7 cm each. Find the number of smaller cubes having only one face painted.

A cube of side length 6 cm is painted red on all its sides. This cube is cut into smaller cubes of side length 2 cm. On each of the smaller cubes, the unpainted sides are painted green. Each of these smaller cubes is now further cut into cubes of side length 1 cm. How many small cubes of side length 1 cm will have exactly 3 of their faces colored green?

A solid cube is painted and cut into 64 smaller but identical pieces by making the minimum possible number of cuts. What is the minimum number of cuts required?