Cathodoluminescence spectroscopy is a key analysis technique in nanophotonics research and technology, yet many aspects of its fundamental excitation mechanisms are not well understood on the single-electron and single-photon level. Here, we determine the cathodoluminescence emission statistics of InGaN quantum wells embedded in GaN under 6-30-keV electron excitation and find that the light emission rate varies strongly from electron to electron. Strong photon bunching is observed for the InGaN quantum well emission at 2.77 eV due to the generation of multiple quantum well excitations by a single primary electron. The bunching effect, measured by the g(2)(t) autocorrelation function, decreases with increasing beam current in the range 3-350 pA. Under pulsed excitation (p=2-100ns; 0.13-6 electrons per pulse), the bunching effect strongly increases. A model based on Monte Carlo simulations is developed that assumes a fraction γ of the primary electrons generates electron-hole pairs that create multiple photons in the quantum wells. At a fixed primary electron energy (10 keV) the model explains all g(2) measurements for different beam currents and pulse durations using a single value for γ=0.5. At lower energies, when electrons cause mostly near-surface excitations, γ is reduced (γ=0.01 at 6 keV), which is explained by the presence of a AlGaN barrier layer that inhibits carrier diffusion to the buried quantum wells. The combination of g(2) measurements in pulsed and continuous mode with spectral analysis provides a powerful tool to study optoelectronic properties and may find application in many other optically active systems and devices.