For studying systems with a cubic anisotropy in interfacial energy σ, we extend the CahnHilliard model by including in it a fourth rank term, which leads to an additional linear term in the evolution equation for the composition field. It also leads to an orientation-dependent effective fourth rank coeficient γ(hkl) in the governing equation for the one-dimensional composition profile across a planar interface. The main effect of a non-negative γ(hkl) is to increase both σ and interfacial width w, each of which, upon suitable scaling, is related to γ(hkl) through a universal scaling function. The anisotropy in the interfacial energy can be large enough to give rise to corners in the Wulff shapes in two dimensions. In particles of finite sizes, the corners get rounded, and their shapes tend towards the Wulff shape with increasing particle size. In the study of unmixing of concentrated alloys, the anisotropy nt only leads to non-spherical particle shapes, but also to strongly elongated morphologies.