A cube is painted red on all its sides. 125 small cubes of equal size are cut from it. How many cubes will have three sides painted?

Given: 

A cube is painted red on all its sides. 125 small cubes of equal size are cut from it.

The dimensions of the original cube.

The cube is cut into 125 smaller cubes, which means:

Number of cubes along one along = $$3\sqrt {125} = 5$$​​

The original cube was a 5 × 5 × 5 cube.

Corner cubes always have 3 sides painted.

A cube has 8 corners where 3 sides meet.

Cubes with 3 sides painted

As there are 8 corners, the number of cubes with 3 painted sides is: 8 cubes

So, a cube has 8 side painted.

Thus, correct option is (d).