Cache enhanced computation offloading as a novel offloading paradigm in mobile edge computing (MEC) can reduce more task execution latency than traditional computation offloading by reusing of computation offloading data. However, existing works only focus on the enhancement between computation offloading and data caching but ignore the competition for cache resources between them. To this end, in this paper, we propose a caching enhanced computation offloading algorithm in mobile edge service networks (MESN), by considering the cache resources competition. We formulate a joint optimization problem of content caching and cache-enhanced computation offloading. Furthermore, we give the optimal caching strategy to achieve the equilibrium between the resources competition. By our offloading algorithm caching strategy, the average response time of computation and content request tasks can get further reduction. In addition, we design two low time complexity algorithms, i.e., mixed caching algorithm and enhanced offloading algorithm, to solve the sub-problems, i.e., smart base station (SBS) caching sub-problem and computation offloading sub-problem, transformed by the original optimization problem. The simulation results show that our algorithms can quickly converge and our scheme can reduce 20.52% average response time of all tasks at most compared with other schemes.