The notion of pyramidal polycubes, namely the piling-up of bricks of a non-increasing size, generalizes in R^n the concept of trapezoidal polyominoes. In the present paper, we prove that n-dimensional dominoes can tile a pyramidal polycube if and only if the latter is balanced, that is, if the number of white cubes is equal to the number of black ones for a chessboard-like coloration, generalizing the result of [BC92] when n=2.