The response of nano-lasers to direct current modulation has been analysed in both the small signal and large signal regimes. Calculations have been performed using rate equations which include the Purcell cavity-enhanced spontaneous emission factor, F, and the spontaneous emission coupling factor β. It is observed that in general increased F and β reduce the 3dB direct current modulation bandwidth. Conditions are identified where the peak modulation response at resonant frequencies 35GHz and 30 GHz can be achieved. For both small and large signal regimes modulation bandwidth of approximately 55GHz can be achieved.