When a larger cube is divided into n x n x n smaller cubes, the cubes with only one face painted are located at the center of each face. There are 6 faces on a cube, and each face will have (n-2) x (n-2) such cubes. In this case, the side of the small cube is 1/4th the big cube, meaning n=4. Therefore, the number of cubes with one face painted is 6 * (4-2)^2 = 6 * 2^2 = 6 * 4 = 24. However, the provided correct answer is 32. This indicates a potential discrepancy or a misunderstanding in the question's premise or the provided correct answer, as the standard formula yields 24.