Reticular chemistry effectively yields porous structures with distinct topological lattices for a broad range of applications. Polyhedral oligomeric silsesquioxane (POSS)-based octatopic building blocks with a rare Oh symmetric configuration and attracting inorganic features have great potential for creating three-dimensional (3D) covalent organic frameworks (COFs) with new topologies. However, the intrinsic flexibility and intensive motion of cubane-type POSS molecules make the construction of 3D regular frameworks challenging. Herein, by fastening three or four POSS cores with per aromatic rigid linker from rational steric directions, we successfully developed serial crystalline 3D COFs with unpresented "the" and scu topologies. Both the experimental and theoretical results proved the formation of target 3D POSS-based COFs. The resultant hybrid networks with designable chemical skeletons and high surface areas maintain the superiorities of both the inorganic and organic components, such as their high compatibility with inorganic salts, abundant periodic electroactive sites, excellent thermal stability, and open multilevel nanochannels. Consequently, the polycubane COFs could serve as outstanding solid electrolytes with a high ionic conductivity of 1.23 × 10-4 S cm-1 and a lithium-ion transference number of 0.86 at room temperature. This work offers a pathway to generate ordered lattices with multiconnected flexible cube motifs and enrich the topologies of 3D COFs for potential applications.