Path planning is a crucial component for realizing the autonomy of mobile robots. However, due to limited computational resources on mobile robots, it remains challenging to deploy state-of-the-art methods and achieve real-time performance. To address this, we propose P3Net (PointNet-based Path Planning Networks), a lightweight deep-learning-based method for 2D/3D path planning, and design an IP core (P3NetCore) targeting FPGA SoCs (Xilinx ZCU104). P3Net improves the algorithm and model architecture of the recently-proposed MPNet. P3Net employs an encoder with a PointNet backbone and a lightweight planning network in order to extract robust point cloud features and sample path points from a promising region. P3NetCore is comprised of the fully-pipelined point cloud encoder, batched bidirectional path planner, and parallel collision checker, to cover most part of the algorithm. On the 2D (3D) datasets, P3Net with the IP core runs 24.54-149.57x and 6.19-115.25x (10.03-59.47x and 3.38-28.76x) faster than ARM Cortex CPU and Nvidia Jetson while only consuming 0.255W (0.809W), and is up to 1049.42x (133.84x) power-efficient than the workstation. P3Net improves the success rate by up to 28.2% and plans a near-optimal path, leading to a significantly better tradeoff between computation and solution quality than MPNet and the state-of-the-art sampling-based methods.