In cloud radio access networks (C-RANs), a substantial amount of data must be exchanged in both backhaul and fronthaul links, which causes high power consumption and poor quality of service (QoS) experience for real-time services. To solve this problem, a cluster content caching structure is proposed in this paper, which takes full advantage of distributed caching and centralized signal processing. In particular, redundant traffic on the backhaul can be reduced because the cluster content cache provides a part of required content objects for remote radio heads (RRHs) connected to a common edge cloud. Tractable expressions for both effective capacity and energy efficiency performance are derived, which show that the proposed structure can improve QoS guarantees with a lower power cost of local storage. Furthermore, to fully explore the potential of the proposed cluster content caching structure, the joint design of resource allocation and RRH association is optimized, and two distributed algorithms are accordingly proposed. Simulation results verify the accuracy of the analytical results and show the performance gains achieved by cluster content caching in C-RANs.