A green wooden cube with an edge of 3 cm was sawn into cubes with an edge of 1 cm.

A green wooden cube with an edge of 3 cm was sawn into cubes with an edge of 1 cm. How many cubes were painted on three sides? On both sides? One side.

We multiply the length of the original cube by the width, and then by the height, we get: the original cube was cut into 27 cubes with an edge of 1 cm.
Since the cube has 8 vertices, the number of cubes colored on three sides is 8.
We remove these 8 cubes, one cube remains on all 12 edges of the original cube. So, the number of cubes painted on both sides is 12.
We remove these 12 cubes, on each face of the original cube there is one cube left. So, the number of cubes colored on one side is 6.
Answer: 8, 12, 6.