The ever-continuing explosive growth of on-demand content requests has imposed great pressure on mobile/wireless network infrastructures. To ease congestion in the network and increase perceived user experience, caching popular content closer to the end-users can play a significant role and as such this issue received significant attention over the last few years. Additionally, energy efficiency is treated as a fundamental requirement in the design of next-generation mobile networks. However, there has been little attention to the overlapping area between energy efficiency and network caching especially when considering multipath routing. To this end, this paper proposes an energy-efficient caching with multipath routing support. The proposed scheme provides a joint anchoring of popular content into a set of potential caching nodes with optimized multi-path support whilst ensuring a balance between transmission and caching energy cost. The proposed model also considers different content delivery modes, such as multicast and unicast. Two separated Integer-Linear Programming (ILP) models are formulated for each delivery mode. To tackle the curse of dimensionality we then provide a greedy simulated annealing algorithm, which not only reduces the time complexity but also provides a competitive performance as ILP models. A wide set of numerical investigations has shown that the proposed scheme is more energy-efficient compared with other widely used approaches in caching under the premise of network resource limitation.