This paper investigates whether observations of seismic anisotropy are compatible with a cubic structure of the inner core Fe alloy. We assume that anisotropy is the result of plastic deformation within a large scale flow induced by preferred growth at the inner core equator. Based on elastic moduli from the literature, bcc- or fcc-Fe produce seismic anisotropy well below seismic observations ($\textless{}0.4\%$). A Monte-Carlo approach allows us to generalize this result to any form of elastic anisotropy in a cubic system. Within our model, inner core global anisotropy is not compatible with a cubic structure of Fe alloy. Hence, if the inner core material is indeed cubic, large scale coherent anisotropic structures, incompatible with plastic deformation induced by large scale flow, must be present.