Cesium lead bromide perovskite (CsPbBr3) nanocrystals have raised impressive interest as efficient and stable optoelectronic materials. Size and morphology play important roles in the final performances of these materials and advanced characterization studies are needed to elucidate structural and surface properties. In this work, CsPbBr3 cubic nanocrystals were obtained by colloidal synthesis and characterized by multinuclear Solid State NMR (SSNMR), complemented by X-Ray Diffraction (XRD), Transmission Electron Microscopy (TEM) and optical spectroscopy. The multinuclear NMR approach allowed the different components of the nanocubes to be separately observed. In particular, the surface ligands and their interactions with the nanocubes surface were investigated by H-1 and C-13 NMR experiments, while the structural investigation of the perovskite nanocubes was addressed by exploiting Pb-207 and Cs-133 spectral properties in comparison with bulk CsPbBr3. Static Pb-207 NMR spectra indicated a possible contribution of chemical shift anisotropy from the Pb-207 nuclei of the outer layer. The Cs-133 NMR spectra showed signals with different chemical shifts for cesium atoms in at least three regions of the nanocubes, from the inner core to the surface, which were interpreted in terms of cubic layers with different distances from the surface using a simple geometrical model. This interpretation was also supported by Cs-133 longitudinal relaxation time measurements.