Inorganic zero-dimensional perovskites, such as Cs4PbBr6, offer an underexplored opportunity to achieve efficient exciton formation and radiative recombination. In particular, the origin of sub-bandgap green emission from Cs4PbBr6 is not well understood. Herein, we develop a sequential deposition approach to growing highly smooth Cs4PbBr6 films with low rms roughness of 8.15 nm by thermal evaporation. We find that the films have an excitonic absorption edge at 3.9 eV, but exhibit sub-bandgap photoluminescence at 2.4 eV, with a photoluminescence quantum yield as high as 55 +/- 2%. We analyze the origin of this sub-bandgap photoluminescence through in-depth transmission electron microscopy, selective area electron diffraction, energy-dispersive X-ray spectrometry, photothermal deflection spectroscopy, and photoluminescence. From these measurements, we find that the Cs4PbBr6 contains residual CsPbBr3, and the wider bandgap Cs4PbBr6 confines the excitons in the Cs4PbBr3, enabling high photoluminescence quantum yields. We use this material as the active layer in light-emitting diodes, achieving an improved external quantum efficiency of 0.36%, a significant improvement over the Cs4PbBr3 control devices with EQEs up to 0.0062%.