Cube of side 12 cm cut into 4&sup3; = 64 small cubes of side 3 cm each.<br><br>
Cubes with exactly 2 painted faces lie on the edges, excluding the corners.<br>
Each edge has 4 cubes; the 2 corner cubes have 3 painted faces.<br>
Cubes per edge with 2 faces = 4 − 2 = 2.<br>
12 edges × 2 = 24 cubes.<br><br>
Volume of one small cube = 3&sup3; = 27 cm&sup3;<br>
Total volume = 24 × 27 = 648 cm&sup3;<br><br>
Final Answer: 24 cubes, 648 cm&sup3;