A series of sixty hitherto unknown cubic lead and tin halide perovskites with the saturated heterocyclic cations (CH2)(n)PH2+ and (CH2)(n)SH+, (n = 2-6) is modeled using periodic DFT approach for the first time. We find that the proposed species are direct bandgap semiconductors with the lattice constants varying from 6.01 angstrom to 7.71 angstrom and absorption wavelengths covering the energy range [1.39-5.26] eV. The estimated masses and velocities of charge carriers amount to similar to m(e) and similar to 10(5) m/s, respectively. Electronic properties of the proposed compounds are compared with that of the previously described lead and tin halide perovskites with the saturated heterocyclic cations (CH2)(n)NH2+ and (CH2)(n)OH+, (n = 2-6). The proposed compounds considerably expand the family of photoactive hybrid metal-halide perovskites.