Non-Orthogonal Multiple Access (NOMA) has been identified as essential in boosting system throughput to meet future wireless communication demands. Maximizing the system throughput in the NOMA network depends on distributing appropriate transmit power from the base station (BS) to users. In the NOMA network, the effective execution of power allocation (PA) at the transmitter and the successful interference cancellation (SIC) process at the receiver are inextricably connected. Therefore, our study presents an optimization problem for efficient PA for maximum sum rate in a downlink NOMA system considering the SIC. Specifically, we investigate an optimization problem to maximize the sum rate by achieving optimal PA with SIC and power budget constraints for downlink NOMA networks. The optimal PA is obtained by finding the common region between the upper bounds for the power budget and SIC constraints. A fast and low-complexity algorithm is proposed for real-world NOMA networks. Finally, simulation results are provided for the proposed method, and compare the results with the benchmark method.