  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 works have only focused on
communication and computation costs, but do not account for 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, compression and caching (C$3$) with a Quality of Information
(QoI) guarantee in a communication network. {Our goal is to identify the
optimal data compression rate and data placement over the network to minimize
the overall energy consumption in the network.} he formulated problem is a
\emph{Mixed Integer Non-Linear Programming} (MINLP) problem with non-convex
functions, which is NP-hard in general. } {We} propose a variant of spatial
branch and bound algorithm (V-SBB), that can {provide} the $\epsilon$-global
optimal solution to {our problem}. {We numerically show that our C3
optimization framework can improve the energy efficiency up to 88\% compared to
any C2 optimization between communication and computation or caching.
Furthermore, for our energy consumption problem, V-SBB {provides comparatively
better solution than some other MINLP solvers.}}
