Energy efficiency is a fundamental requirement of modern data-communication systems, and its importance is reflected in much recent work on performance analysis of system energy consumption. However, most work has only focused on communication and computation costs without accounting for data caching costs. Given the increasing interest in cache networks, this is a serious deficiency. In this paper, we consider the problem of energy consumption in data communication, computation and caching (C3) with a quality-of-information (QoI) guarantee in a communication network. Our goal is to identify the optimal data compression rates and cache placement over the network that minimizes the overall energy consumption in the network. We formulate the problem as a mixed integer nonlinear programming (MINLP) problem with nonconvex functions, which is non-deterministic polynomial-time hard (NP-hard) in general. We propose a variant of the spatial branch-and-bound algorithm (V-SBB) that can provide an ϵ-global optimal solution to the problem. By extensive numerical experiments, we show that the C3 optimization framework improves the energy efficiency by up to 88% compared to any optimization that only considers either communication and caching or communication and computation. Furthermore, the V-SBB technique provides comparatively better solutions than some other MINLP solvers at the cost of additional computation time.