Multiple luminescence peaks emitted by a single InGaN/GaN quantum-well(QW) nanorod, extending from the blue to the red, were analysed by a combination of electron microscope based imaging techniques. Utilizing the capability of cathodoluminescence hyperspectral imaging it was possible to investigate spatial variations in the luminescence properties on a nanoscale. The high optical quality of a single GaN nanorod was demonstrated, evidenced by a narrow band-edge peak and the absence of any luminescence associated with the yellow defect band. Additionally two spatially confined broad luminescence bands were observed, consisting of multiple peaks ranging from 395 nm to 480 nm and 490 nm to 650 nm. The lower energy band originates from broad c-plane QWs located at the apex of the nanorod and the higher energy band from the semipolar QWs on the pyramidal nanorod tip. Comparing the experimentally observed peak positions with peak positions obtained from plane wave modelling and 3D finite difference time domain(FDTD) modelling shows modulation of the nanorod luminescence by cavity modes. By studying the influence of these modes we demonstrate that this can be exploited as an additional parameter in engineering the emission profile of LEDs.