A cache-aided $K$-user Gaussian broadcast channel (BC) is considered. The transmitter has a library of $N$ equal-rate files, from which each user demands one. The impact of the equal-capacity receiver cache memories on the minimum required transmit power to satisfy all user demands is studied. Considering uniformly random demands across the library, both the minimum average power (averaged over all demand combinations) and the minimum peak power (minimum power required to satisfy all demand combinations) are studied. Upper bounds are presented on the minimum required average and peak transmit power as a function of the cache capacity considering both centralized and decentralized caching. The lower bounds on the minimum required average and peak power values are also derived assuming uncoded cache placement. The bounds for both the peak and average power values are shown to be tight in the centralized scenario through numerical simulations. The results in this paper show that proactive caching and coded delivery can provide significant energy savings in wireless networks.