Effective properties of polycrystals are often estimated by taking into account solely the intrinsic variabilities in crystallographic orientations along with those of the morphological shapes of the grains. The variability on the single crystal elastic moduli is not considered. In this work, we calculated the analytical estimates for effective elastic moduli of numerically generated equiaxed cubic polycrystals. The influence of the variability of the components of the single crystal elasticity tensor on the statistical properties of the homogenized macroscopic stiffness tensor is investigated.