The electronic structure of the Goldberg silicon quantum dots with central symmetric hollows and their endohedral complexes with erbium was studied using DFT with and without the strong electron correlations, whose inclusion was found to determine the binding energy. Based on optimized DFT structures, we were able to explain the details of Er-doped nanocrystalline silicon made in experiment. The role of symmetry of the central hollows in quantum dots was elucidated, and the key features of the density of states are explained, providing information for the tuning and design of Er-doped silicon light emitters.