An unusually sharp localized surface plasmon resonance (sLSPR) is observed for a monolayer of glass-supported silver nanocubes coated with a thin, 5-20 nm, Al2O3 film. The resonance becomes significantly narrower and stronger while losing optical anisotropy and sensitivity to the surroundings with increasing overlayer thickness. Surface-enhanced Raman scattering excitation profiles indicate an additional enhancement to the electric field brought in by the sLSPR. The resonance is thought to originate from a Fano-like constructive interference between the quadrupolar and dipolar LSPR modes in supported silver nanocubes leading to enhanced light extinction. This phenomenon is of significance for plasmon-induced charge-transfer processes in photovoltaics and catalysis.