Herein we detail a novel approach for targeting zeolite-like metal-organic frameworks (ZMOFs) that utilizes metal-organic cubes, which are regarded as double four-membered rings (d4Rs) and are composite building units (BUS) in traditional inorganic zeolites. Accordingly, we outline the successful implementation of this strategy by reporting two ZMOFs with ACO and AST zeolite-like topologies, which were constructed from d4R BUS exclusively held together by hydrogen bonds. Their porosity was evaluated, delineating high hydrogen uptake and exceptional stability for the two hydrogen-bonded materials.