The colloidal processing of nearly monodisperse and highly crystalline single-domain ferroelectric or ferromagnetic nanocubes is a promising route to produce superlattice structures for integration into next-generation devices, whereas controlling the local behaviour of nanocrystals is imperative for fabricating highly-ordered assemblies. The current picture of nanoscale polarization in individual nanocrystals suggests a potential presence of a significant dipolar interaction, but its role in the condensation of nanocubes is unknown. We simulate the self-assembly of colloidal dipolar nanocubes under osmotic compression and perform the microstructural characterization of their densified ensembles. Our results indicate that the long-range positional and orientational correlations of perovskite nanocubes are highly sensitive to the presence of dipoles.