The phase behavior of 3D assemblies of nanocubes in a ligand-rich solution upon solvent evaporation was experimentally investigated using small-angle x-ray scattering and electron microscopy. We observed a continuous transformation of assemblies between simple cubic and rhombohedral phases, where a variable angle of rhombohedral structure is determined by ligand thickness. We established a quantitative relationship between the particle shape evolution from cubes to quasispheres and the lattice distortion during the transformation, with a pathway exhibiting the highest known packing.