Answer:
There are 598 unpainted cubes.
Step-by-step explanation:
The cube root of 1331 is 11, so the cube is an 11*11*11 cube. Since the volume of the cube is 1331, then we need to find the number of cubes that ARE painted, and subtract that number from 1331. There are 6 faces. On one face, there are 121 cubes that are painted. On the face opposite of the first face, there are also 121 cubes. Then, we count a middle face. There are 121-22 cubes that are painted there, which is 99. On the face opposite of that, there are also 99 faces. Finally, the last 2 faces. One of them has 121-42 cubes that are painted, which is 79, and opposite of that face, there are also 79. 121+121+99+99+79+79=598