With the increasing popularity of mobile video services, cellular networks are shifting their focus from the core network to the edge network to facilitate resource-intensive services and alleviate backhaul burdens. However, due to the overlapping coverage and user similarity in preferences, substantial cache redundancy exisits in edge networks. Moreover, user mobility creates a challenge for device-to-device (D2D) communication, which impacts the richness and hit ratio of the edge cache. This paper proposes a content-adaptive cache partitioning (CACP) strategy for mobile edge networks, which aims to reduce the content accessing cost. We present a two-layer collaborative caching model, which consists of 5G base station (gNB) caching and D2D caching. Furthermore, we design a public and private cache partitioning method for gNBs to improve the richness of local cache, and a static and dynamic cache partitioning method for user devices to address the varying mobility patterns. The simulation results show that the proposed CACP strategy always achieves a low content accessing cost and a comparatively high hit ratio, accompanied by a relatively high energy consumption at the user ends.