Molybdenum-dependent nitrogenase is the most active biological catalyst for dinitrogen reduction. This reaction is catalyzed by a [MoFe7S9C] cofactor (FeMoco). FeMoco can be described as a double-cubane, with [MoFe3S3] and [Fe4S3] parts, bound via an interstitial carbide and three bridging sulfides. Model compounds have been synthesized since early studies of the enzyme and Coucouvanis and co-workers demonstrated that [MoFe3S4] cubanes are active catalysts for many substrates catalyzed by nitrogenase. These reactions include hydrazine reduction to ammonia and cis-dimethyldiazene reduction to methylamine. Experiments implicated molybdenum as the binding site but the mechanisms have not been studied by theoretical calculations before. Here we present a DFT study of the catalytic reaction mechanisms of hydrazine and cis-dimethyldiazene reduction with a [MoFe3S4] cubane. Like in the experiments, molybdenum is revealed as the likely substrate binding site, likely due to the labile ligand on Mo. For the hydrazine mechanism, a reduction event is centered on Fe, specifically on the Fe antiferromagnetically coupled to the mixed-valence pair. After protonation of the distal hydrazine nitrogen, the N-N bond can be cleaved to yield NH3 and a Mo-bound -NH2 intermediate. This is followed by another protonation/reduction step to give an -NH3 intermediate, and finally substituted by the substrate to complete the cycle. The computed mechanisms shed light on the bimetallic cooperativity in these systems where the reduction steps are localized on Fe while the substrate binds to Mo and the reductions require only a free coordination site (on Mo) and a favorable reduction event (to Fe). Although both substrates easily displace the weakly bound acetonitrile ligand, one reduction event is required for hydrazine activation and N-N bond cleavage to give an integer-spin -NH2 intermediate. An integer-spin -NH2 intermediate has been observed as a common intermediate for the enzyme reduction of hydrazine and diazene, suggesting a possible link to the enzyme chemistry.