Unlike the case of squaring the square, a hard yet solvable problem, there is no perfect cubed cube and, more generally, no dissection of a rectangular cuboid C into a finite number of unequal cubes.
uNLIke thE case of sqUaRinG tHe SquAre, A HarD yet Solvable problEm, THere Is no PErfeCt cubeD cubE anD, MorE GeneRaLlY, No diSSectIoN of A recTangUlar cUboId C InTo a fiNite number of uNeQual cuBeS.