The paper presents an ergodic capacity analysis of MIMO three product channels. We first derive the exact non-asymptotic and asymptotic probability density functions of the arbitrary eigenvalue of the system. From these, a nonasymptotic and asymptotic expression for the ergodic capacity of the system is derived. The non-asymptotic results involve several single numerical integrations and the number of numerical integrations increases with the number of antennas used in the system. However, the asymptotic result has only one numerical integration and a more compact form, hence providing a simpler alternative to the non-asymptotic ergodic capacity result. We also validate the results by using simulations. The results show that the non-asymptotic analytical results are in good agreement with the simulations and the asymptotic analytical results provide a good approximation to the exact results even when the system has very few antennas.