Cooperation between the fog and cloud in fog-enabled radio access network could enormously improve the computation offloading services both in terms of latency and energy consumption, while edge caching allowing for low-latency transmission of the cached files, is essential for cooperation. It is necessary to select the best method that minimizes the energy consumption with latency tolerance guaranteed, to offload the task. In this paper, we study the problem of content placement for edge caching and the cooperative computation offloading between the fog and the cloud by optimizing the cooperative offloading decisions and caching strategies. The problem is formulated to minimize the total energy consumption of all the UEs by optimizing the transmit power of the user equipments (UEs), caching strategies and the cooperation factor (the ratio of the fog execution of a file to the whole file), which is a non-convex programming problem. An approximate solution is obtained by using successive convex approximation strategy and implicit enumeration method. Numerical results show that our proposed algorithm can achieve better performance compared with other schemes, e.g., cloud computing and cache most popular strategies.