We report here an extensive high pressure small-angle X-ray scattering study on 3D supercrystals self-assembled from colloidal spherical gold crystalline nanoparticule (NPs). We used a large variety of NPs with different gold core diameter, from 2 to 10 nm, grafted with different ligands: alkane-thiols or oleylamine. The self assembly of these various NPs leads to supercrystals of different structures: face centered cubic (FCC), body centered cubic (BCC), as well as the C14 Frank and Kasper phase. Using a Diamond Anvil Cell to apply pressure on these wide range of samples, we provide a unique overview on the mechanical properties of gold NPs supercrystals. In particular, bulk modulii have been determined from low pressure regime and the different behavior between FCC and BCC structures has been interpreted as due to an easier restructuring of the ligand conformation in the FCC structure compared to the BCC structure. At higher pressure, a fingerprint of irreversible structural transition has been observed. We have ascribed this irreversibility to the sintering of nanoparticles and confirmed this interpretation by transmission electron microscopy.