We used proton ( (1)H nuclear magnetic relaxation (NMR) dispersions to study the molecular dynamics in the isotropic phase and mesophases (nematic and columnar hexagonal) of a supermesogenic octapode formed by laterally connecting calamitic mesogens to an inorganic silsesquioxane cube through flexible spacers. The dispersions of the spin-lattice relaxation time (T(1)) are interpreted through relaxation mechanisms used for the study of molecular dynamics in low-molar-mass liquid crystals but adapted to the case of liquid crystalline supermolecules. At high frequencies (above 10MHz) the behaviour of the T(1) with the Larmor frequency is similar for all phases and is ascribed to local reorientations and/or rotations. At intermediate and low frequencies (below 10MHz) our results show notable differences in the T(1) behaviour with respect to the mesophases. The nematic (N) and isotropic (Iso) phases' low-frequency results are similar and are interpreted for both phases in terms of order director fluctuations (ODF), revealing that even in the isotropic phase local nematic order is detected by proton NMR relaxometry. Local nematic order in the Iso phase is interpreted in terms of the presence of nematic cybotactic clusters induced by the interdigitation of mesogens that is promoted by the silsesquioxane octapode molecular structure. In the columnar hexagonal (Col (h) phase, the T(1) dispersions show that elastic columnar deformations (ECD) dominate the nuclear magnetic relaxation below 10MHz. This result shows that the columnar packing of the octapode clearly restricts the collective fluctuations of the mesogenic units inspite of their local nematic order.