Assemblies of strongly interacting metallic nanoparticles are the basis for plasmonic nanostructure engineering. We demonstrate that clusters of four identical spherical particles self-assembled into a close-packed asymmetric quadrumer support strong Fano-like interference. This feature is highly sensitive to the polarization of the incident electric field due to orientation-dependent coupling between particles in the cluster. This structure demonstrates how careful design of self-assembled colloidal systems can lead to the creation of new plasmonic modes and the enabling of interference effects in plasmonic systems.