NMR line shapes of the lipid and aqueous species in bicontinuous cubic phase (BCP) samples prepared by centrifugation are inhomogeneously broadened. The broadening of the lipid peaks is removed by magic-angle spinning (MAS). In this work, we studied the mechanism of this broadening using H-1 and C-13 NMR spectroscopy of a myverol/water BCP. It is demonstrated that the inhomogeneity possesses an intrinsic contribution that is independent of instrumental or setup factors and can be attributed to the microscopic organization of the BCP bilayer. A mechanism of the inhomogeneous broadening is proposed, which involves a spatially nonuniform diamagnetically induced magnetic field determined by the mesoscopic structure and the diamagnetic susceptibilities of the two BCP domains. The proposed mechanism does not require that molecular reorientation of the lipid be slow for the inhomogeneous broadening to survive. We discuss how this inhomogeneous broadening can be employed as a probe of compositional uniformity and microscopic organization of BCP samples.