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. Assuming uncoded cache placement, a lower bound on the required transmit power as a function of the cache capacity is derived. An achievable centralized caching scheme is proposed, which not only utilizes the user's local caches, but also exploits the correlation among the contents in the database. The performance of the scheme, which provides an upper bound on the required transmit power for a given cache capacity, is characterized. Our results indicate that exploiting the correlations among the contents in a cache-aided Gaussain BC can provide significant energy savings.