Colloidal CsPbBr3 nanocrystals (NCs) have emerged as promising candidates for various opto-electronic applications, such as light-emitting diodes, photodetectors, and solar cells. Here, we report on the self-assembly of cubic NCs from an organic suspension into ordered cuboidal supraparticles (SPs) and their structural and optical properties. Upon increasing the NC concentration or by addition of a nonsolvent, the formation of the SPs occurs homogeneously in the suspension, as monitored by in situ X-ray scattering measurements. The three-dimensional structure of the SPs was resolved through high-angle annular dark-field scanning transmission electron microscopy and electron tomography. The NCs are atomically aligned but not connected. We characterize NC vacancies on superlattice positions both in the bulk and on the surface of the SPs. The occurrence of localized atomic-type NC vacancies - instead of delocalized ones - indicates that NC-NC attractions are important in the assembly, as we verify with Monte Carlo simulations. Even when assembled in SPs, the NCs show bright emission, with a red shift of about 30 meV compared to NCs in suspension.