We propose a technique to reduce compulsory misses of packet processing cache (PPC), which largely affects both throughput and energy of core routers. Rather than prefetching data, our technique called response prediction cache (RPC) speculatively stores predicted data in PPC without additional access to the low-throughput and power-consuming memory (i.e., TCAM). RPC predicts the data related to a response flow at the arrival of the corresponding request flow, based on the request-response model of internet communications. Our experimental results with 11 real-network traces show that RPC can reduce the PPC miss rate by 13.4% in upstream and 47.6% in downstream on average when we suppose three-layer PPC. Moreover, we extend RPC to adaptive RPC (A-RPC) that selects the use of RPC in each direction within a core router for further improvement in PPC misses. Finally, we show that A-RPC can achieve 1.38x table-lookup throughput with 74% energy consumption per packet, when compared to conventional PPC.