Step 1: Classify the 27 small cubes by position. Corner cubes: 8, each with 3 painted faces. Step 2: Cubes in the middle of each edge have exactly 2 painted faces. A cube has 12 edges, and each 3 cm edge has (3 − 2) = 1 such middle cube. So 12 × 1 = 12. Step 3: Cubes at the centre of each face have 1 painted face: 6 cubes. Step 4: The cube in the very centre has 0 painted faces: 1 cube. Step 5: Check the total: 8 + 12 + 6 + 1 = 27 ✓. Answer: 12.