We investigate and compare the mechanical properties of two micellar cubic crystals. Both are obtained from aqueous triblock-copolymer solutions of similar block structure, (PEO)(76)(PPO)(29)(PEO)(76) and (PEO)(127)(PPO)(48)(PEO)(127), designated Pluronic F68 and F108 respectively. Extensive small angle X-ray scattering experiments under shear and common rheometry provide the following results: (i) the solid phases of the two polymeric solutions are constituted of micelles that are ordered in a bcc (F68) and fee (F108) structure. The overall appearance of both unsheared samples is polycrystalline; (ii) SAXS showed that both systems undergo a structural reorientation under shear, with the dense planes arranged parallel to the velocity - vorticity plane, thus facilitating flow; (iii) F68 showed a clear transition in the flow curve, associated with a textural change, but the F108 system exhibited a continuous evolution; (iv) the bcc crystal appears to have no measurable yield stress and flows even for low applied stresses. This was in contrast to the fcc sample which showed a clear yield stress, separating creep and flow regimes.