Plasmonic nanocubes are ideal candidates in realizing controllable reflectance surfaces, unidirectional nanoantennas and other plasmon-associated applications. In this work, we perform full-wave calculations of the optical forces in three- dimensional gold nanocube dimers. For a fixed center-to-center separation, the rotation of the plasmonic nanocube leads to a slight shift of the plasmonic resonance wavelength and a strong change in the optical binding forces. The effective gap and the near field distribution between the two nanocubes are shown to be crucial to this force variation. We further find that the optical binding force is dominated by the scattering process while the optical forces in the wavevector direction are affected by both scattering and absorption, making the former relatively more sensitive to the rotation of (an effective gap between) the nanocubes. Our results would be useful for building all-optically controllable meta-surfaces.