A cube has edge-length of 8 cm. Cut in into several identical cubes so that their total surface area is 5 times that of the original cube. What is the volume of one such small cube?
I started b finding the surface area of the 8*8*8 cube, which was 384. I multiplied that by 5 to get 1920. I prime factorized 1920 into $2^7 \cdot 3 \cdot 5$. I'm stuck at this point, and it doesn't seem like a cube that can be split up to have these factors.