Interest in creating magnetic metamaterials has led to methods for growing superstructures of magnetic nanoparticles. Mesoscopic crystals of maghemite (gamma-Fe2O3) nanoparticles can be arranged into highly ordered body-centered tetragonal lattices of up to a few micrometers. Although measurements on disordered ensembles have been carried out, determining the magnetic properties of individual mesoscopic crystals is challenging due to their small total magnetic moment. Here, we overcome these challenges by utilizing sensitive dynamic cantilever magnetometry to study individual micrometer-sized gamma-Fe2O3 mesocrystals. These measurements reveal an unambiguous cubic anisotropy, resulting from the crystalline anisotropy of the constituent maghemite nanoparticles and their alignment within the mesoscopic lattice. The signatures of anisotropy and its origins come to light because we combine the self-assembly of highly ordered mesocrystals with the ability to resolve their individual magnetism. This combination is promising for future studies of the magnetic anisotropy of other nanoparticles, which are too small to investigate individually.