The Fano interference phenomenon between localized surface plasmon resonances (LSPRs) of individual silver nanocubes is investigated using dark-field optical microscopy and electron-energy loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM). By computing the polarization induced by the electron beam, we show that the hybridized modes responsible for this Fano interference are the same as those present in the resonance-Rayleigh scattering spectrum of an individual nanocube on a substrate.