Grazing incidence small-angle scattering and electron microscopy have been used to show for the first time that nonspherical nanoparticles can assemble into highly ordered body-centered tetragonal mesocrystals. Energy models accounting for the directionality and magnitude of the van der Waals and dipolar interactions as a function of the degree of truncation of the nanocubes illustrated the importance of the directional dipolar forces for the formation of the initial nanocube clusters and the dominance of the van der Waals multibody interactions in the dense packed arrays.