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?

A cuboid of dimensions 24 cm × 18 cm × 12 cm has all its faces painted blue. It is cut into smaller cubes, each having a volume of 8 cm3. Find the relationship that correctly gives the number of small cubes having only one face painted.