Nanostructuring the perovskite oxide SrTiO3via 3D assemblage of nanocubes is shown to lower the thermal conductivity over a broad range of temperatures. This is particularly valuable in thermoelectric material applications. The assemblages are composed of pristine perovskite grain interiors confined by SrO or TiO2-rich interfaces resembling Ruddlesden Popper and Magneli phases. The optimum performance in terms of the thermoelectric device applications are predicted to come from SrTiO3 nanocubes synthesised in a Sr-rich environment, although TiO2-rich nanocubes would have an increased strength. The vibrational fingerprint of the assemblages, characterized by a combination of lattice and molecular dynamics, display the characteristic modes of the perovskite structure and significant interface vibrational modes, some at very low frequency. TiO2-rich assemblages display splitting of the active modes similar to anatase providing a way to distinguish them from SrO-rich assemblages. Finally, we show that the IR active low vibrational frequencies are sensitive to the structure and stacking of the nanocubes indicating that it could be an efficient experimental route for identifying and characterizing the material with very low thermal conductivity.