How many solid cubes of edge 6 cm can be packed inside an open box measuring 25 cm by 20 cm by 15 cm, if no cube may be cut and every cube must sit square to the sides?

Count along each edge separately and keep only whole cubes: 25/6 = 4.16 → 4, 20/6 = 3.33 → 3, 15/6 = 2.5 → 2. That gives $4\times 3\times 2=24$ cubes, and strips of 1 cm, 2 cm and 3 cm are wasted along the three directions. (Dividing volume by volume, 7500/216 = 34.7 → 34, assumes the leftover slivers can be reassembled, which they cannot; 36 rounds 2.5 up to 3; 40 rounds two of the three counts up.)