This work studies the joint problem of content placement, remote radio head (RRH) clustering and beamformer design, in a cache-enabled cloud-radio access network (C-RAN). In the considered system, downlink users are cooperatively served by multiple RRHs, in turn connected to a centralized baseband unit (BBU) pool via fronthaul links. Each RRH is equipped with a local cache from which it can directly acquire the requested user contents, without utilizing the fronthaul links. We aim to jointly optimize the aforementioned three aspects, in order to strike a balance between fronthaul traffic reduction and transmission power minimization. To this end, we propose to employ the ratio between these two important system utilities as the objective function, referred to as caching efficiency. Two joint design algorithms are presented to address the resulting nonconvex optimization problem, which features coupling constraints and mixed-integer variables, namely: the penalty concave-convex procedure (P-CCCP) and penalty dual decomposition (PDD) based algorithms. Furthermore, since content placement is usually updated over a larger timescale, we propose a two-timescale joint design algorithm, where the P-CCCP and PDD-based algorithms can be employed for efficient initialization as well as for establishing performance limits. Simulation results validate the efficiency of the proposed algorithms.