The resurgence of interest in the hydrogen economy could hinge on the distribution of hydrogen in a safe and efficient manner. Whilst great progress has been made with cryogenic hydrogen storage or liquefied ammonia, liquid organic hydrogen carriers (LOHCs) remain attractive due to their lack of need for cryogenic temperatures or high pressures, most commonly a cycle between methylcyclohexane and toluene. Oxidation of methylcyclohexane to release hydrogen will be more efficient if the equilibrium limitations can be removed by separating the mixture. This report describes a family of six ternary and quaternary multicomponent metal–organic frameworks (MOFs) that contain the three‐dimensional cubane‐1,4‐dicarboxylate (cdc) ligand. Of these MOFs, the most promising is a quaternary MOF (CUB‐30), comprising cdc, 4,4′‐biphenyldicarboxylate (bpdc) and tritopic truxene linkers. Contrary to conventional wisdom that adsorptive interactions with larger, hydrocarbon guests are dominated by π–π interactions, here we report that contoured aliphatic pore environments can exhibit high selectivity and capacity for LOHC separations at low pressures. This is the first time, to the best of our knowledge, where selective adsorption for cyclohexane over benzene is witnessed, underlining the unique adsorptive behavior afforded by the unconventional cubane moiety.