Using the first-principles based density functional tight-binding (DFTB) method with our newly developed Si-Si, Ge-Ge and Si-Ge parameters for thermal properties calculations, the in-plane and cross-plane thermal conductivities of Si/Ge superlattices with ideal interfaces are directly calculated. The calculated in-plane and cross-plane thermal conductivities of Si/Ge superlattices show different trends compared to the previous predictions from the virtual crystal approximation. Moreover, the effect of mass and bond variances on reducing in-plane and cross-plane thermal conductivities are studied separately. We find that mass variance has more profound impacts on the cross-plane thermal conductivities reduction by enhancing the interface phonon scattering. But when the mass variance is absent, the in-plane thermal conductivities of Si/Ge superlattices are unexpectedly lower than the cross-plane ones. These results shed light on new understandings of phonon transport in Si/Ge superlattices.