Explosive growth of mobile data demand may impose a heavy traffic burden on fronthaul links of cloud-based small cell networks (C-SCNs), which deteriorates users' quality of service (QoS) and requires substantial power consumption. This paper proposes an efficient maximum distance separable (MDS) coded caching framework for a cache-enabled C-SCNs, aiming at reducing long-term power consumption while satisfying users' QoS requirements in short-term transmissions. To achieve this goal, the cache resource in small-cell base stations (SBSs) needs to be reasonably updated by taking into account users' content preferences, SBS collaboration, and characteristics of wireless links. Specifically, without assuming any prior knowledge of content popularity, we formulate a mixed timescale problem to jointly optimize cache updating, multicast beamformers in fronthaul and edge links, and SBS clustering. Nevertheless, this problem is anti-causal because an optimal cache updating policy depends on future content requests and channel state information. To handle it, by properly leveraging historical observations, we propose a two-stage updating scheme by using Frobenius-Norm penalty and inexact block coordinate descent method. Furthermore, we derive a learning-based design, which can obtain effective tradeoff between accuracy and computational complexity. Simulation results demonstrate the effectiveness of the proposed two-stage framework.