Content delivery in a multi-user cache-aided broadcast network is studied, where a server holding a database of correlated contents communicates with the users over a Gaussian broadcast channel (BC). The minimum transmission power required to satisfy all possible demand combinations is studied, when the users are equipped with caches of equal size. Two centralized caching schemes are proposed, both of which not only utilize the user's local caches, but also exploit the correlation among the contents in the database. The first scheme implements uncoded cache placement and delivers coded contents to users using superposition coding. The second scheme, which is proposed for small cache sizes, places coded contents in users' caches and jointly encodes the cached contents of users and the messages targeted at them. The performance of the proposed schemes, which provide upper bounds on the required transmit power for a given cache capacity, is characterized. The scheme based on coded placement improves upon the first one for small cache sizes, and under certain conditions meets the uncoded placement lower bound. A lower bound on the required transmit power is also presented assuming uncoded cache placement. Our results indicate that exploiting the correlations among the contents in a cache-aided Gaussian BC can provide significant energy savings.