Given a heterogeneous social network, can we forecast its future? Can we predict who will start using a given hashtag on twitter? Can we leverage side information, such as who retweets or follows whom, to improve our membership forecasts? We present TENSORCAST, a novel method that forecasts time-evolving networks more accurately than the current state of the art methods by incorporating multiple data sources in coupled tensors. TENSORCAST is (a) scalable, being linearithmic on the number of connections; (b) effective, achieving over 20% improved precision on top-1000 forecasts of community members; (c) general, being applicable to data sources with a different structure. We run our method on multiple real-world networks, including DBLP and a Twitter temporal network with over 310 million nonzeros, where we predict the evolution of the activity of the use of political hashtags.