Recent years, Software Defined Routers (SDRs) (programmable routers) have emerged as a viable solution to provide a cost-effective packet processing platform with easy extensibility and programmability. Multi-core platforms significantly promote SDRs' parallel computing capacities, enabling them to adopt artificial intelligent techniques, i.e., deep learning, to manage routing paths. In this paper, we explore new opportunities in packet processing with deep learning to inexpensively shift the computing needs from rule-based route computation to deep learning based route estimation for high-throughput packet processing. Even though deep learning techniques have been extensively exploited in various computing areas, researchers have, to date, not been able to effectively utilize deep learning based route computation for high-speed core networks. We envision a supervised deep learning system to construct the routing tables and show how the proposed method can be integrated with programmable routers using both Central Processing Units (CPUs) and Graphics Processing Units (GPUs). We demonstrate how our uniquely characterized input and output traffic patterns can enhance the route computation of the deep learning based SDRs through both analysis and extensive computer simulations. In particular, the simulation results demonstrate that our proposal outperforms the benchmark method in terms of delay, throughput, and signaling overhead.