The optical properties of a stack of GaN/AlN quantum discs (QDiscs) in a GaN nanowire have been studied by spatially resolved cathodoluminescence (CL) at the nanoscale (nanoCL) using a scanning transmission electron microscope (STEM) operating in spectrum imaging mode. For the electron beam excitation in the QDisc region, the luminescence signal is highly localized, with spatial extent as low as 5 nm, due to the high band gap difference between GaN and AlN. This allows the discrimination between the emission of neighbouring QDiscs and evidencing the presence of lateral inclusions, about 3 nm thick and 20 nm long rods (quantum rods, QRods), grown unintentionally on the nanowire sidewalls. These structures, also observed by STEM dark-field imaging, are proved to be optically active in nanoCL, emitting at similar, but usually shorter, wavelengths with respect to most QDiscs.