Indium-decorated palladium nanoparticles (In-on-PdNPs) are active for room-temperature catalytic reduction of aqueous nitrate, where the active sites are metallic In atoms on the Pd surface. The PdNPs are pseudo-spherical in shape, and it is unclear if their faceted nature plays a role in nitrate reduction. We synthesized different-sized, cube-shaped NPs with differing In coverages (sc%), and studied the resultant In-on-Pd-nanocubes (NCs) for nitrate reduction. The NCs exhibited volcano-shape activity dependence on In sc%, with peak activity around 65-75 sc%. When rate constants were normalized to undercoordinated atoms (at edge+corners), the NCs exhibited near-identical maximum activity (20×-higher than In-on-PdNPs) at ρIn/Pd edge+corner ~0.5 (~5 In atoms per 10 edge and corner atoms). NCs with a higher In edge+corner density (ρIn/Pd edge+corner ~1.5) were less active but did not generate NH4+ at nitrate conversions tested up to 36%. Edge-decorated cubes may be the structural basis of improved bimetallic catalytic denitrification of water.