Caching popular contents at heterogeneous devices, e.g., fog nodes (FNs) or fog access points (FAPs), constitutes a promising technique of reducing both the traffic and the energy consumption of the backhaul links. In this paper, we propose an energy-efficient caching and node association algorithm for cache-aided fog networks. First, we solve the problem of energy-efficient content caching and delivery in the FNs/FAPs. In both caching scenarios, we investigate the relationship between the caching probability of the file and the energy-efficient content delivery by formulating the associated energy efficiency (EE) optimization problem. Then, we derive a joint modulation mode allocation strategy and caching policy for each content caching node and conceive a joint node association and caching algorithm. Finally, we quantify both the overall EE and throughput for demonstrating that the proposed caching and transmission strategy achieves significant performance improvements.