This study investigates the mechanical behavior of a novel set of Cuboidal Spherical Plate Lattice (CSPL) materials. The procedure of constrained-domain topology optimization is implemented with the aim of enhancing stiffness. The micromechanical finite element homogenization approach is used to evaluate the effective elastic-plastic properties of the CSPLs and their topologically optimized counterparts, TOCSPLs (Topologically Optimized Cuboidal Spherical Plate Lattices). The TOCSPLs demonstrate higher uniaxial, shear, and bulk moduli compared to the CSPLs, with an increase of 31%, 14%, and 36% respectively. Moreover, there is an increase in the yield strengths under uniaxial, shear, and hydrostatic loading conditions, with enhancements of 103%, 55%, and 62%, respectively. The topologies are additively manufactured through Fused Deposition Modeling (FDM) out of ABS thermoplastic material. The quasi-static compression experiments demonstrate the superiority of TOCSPL 111+100 over the other topologies in terms of uniaxial modulus. The suffix 111+100 denotes the crystallographic planar orientations in which the solid plate-like disks were formed within a cubic system. The topologies proposed herein outperform certain types of Triply Periodic Minimal Surface, honeycomb, truss-, and plate-based lattice materials. The proposed topologies offer a compelling justification for their utilization in applications that require load-bearing and impact absorption capabilities.