Problem D

Caen’s Cubes

Caen has a cube with a volume of \(n \text{ cm}^3\). They cut this cube into \(n\) smaller cubes, each with a side length of \(1\) cm. The total surface area of the \(n\) smaller cubes is ten times the surface area of Caen’s original cube. Determine the side length of Caen’s original cube.