We have carried out neutron spectroscopic and diffraction studies on powder samples of several 5d families of cubic double perovskites, that involve Os and Re in different oxidation states. This includes 5d3 systems, such as Ba2YOsO6 with Os5+, 5d2 systems such as Ba2MgOsO6 with Os6+, and the 5d1 system Ba2MgReO6 with Re6+. The 5d3 double perovskites all display well defined Neel order with sizeable dipole magnetic moments, while the 5d1 system displays both a structural and a magnetic transition on lowering temperature, consistent with expectations for coupled quadrupolar and dipolar degrees of freedom. The 5d2 cubic double perovskites are particularly intriguing as these display clear phase transitions at T* ~ 45 K where ~ R ln(2) in entropy is released on passing through T*. However, while magnetic inelastic scattering is clearly observed, there is no evidence for the ordering of dipole moments in neutron diffraction, with an upper limit on any possible ordered dipole moment of ~ 0.1 muB. We understand these results in terms of ferro-octupolar order below T*, and argue that this is consistent with the full set of experimental observations on these 5d2 cubic double perovskites. We believe this likely constitutes the first compelling case for octupolar order in a d-orbital Mott insulator.