The recently introduced cube and scale cube skeleton of Martínez et al. (Graph Models 75:189–207, 2013) are a new type of skeletal representations for polygons or polyhedra enclosed by axis-aligned edges or faces. In this paper, we present efficient algorithms to compute the three-dimensional cube and scale cube skeleton. In addition, we analyze the combinatorial complexity of the three-dimensional cube skeleton. We also introduce the three-dimensional interior cube skeleton, which is homotopically equivalent to the input shape. Finally, we experimentally evaluate the efficiency and robustness of all the presented algorithms and compare the obtained skeletons with other relevant skeletal representations.