Step 1: Original cube: $12 \times 12 \times 12$ (side length). Cut into 36 smaller cubes: 32 small ($2 \times 2 \times 2$), 4 big ($4 \times 4 \times 4$).

Step 2: Big cubes have no blue faces exposed, so we ignore them.

Step 3: Each face of the cube is $12 \times 12 = 144$ square units. Each small cube has $2 \times 2 = 4$ square units per face. So, each face is divided into 36 small cubes.

Step 4: Only the 4 middle cubes on each face have exactly one face painted. 6 faces $\times$ 4 cubes = 24 cubes with one face painted.

Step 5: Since the question asks about cubes that only have one face painted, the correct answer is 8.