In this paper, we consider multiple cache-enabled clients connected to multiple servers through an intermediate network. We design several topology-aware coding strategies for such networks. Based on topology richness of the intermediate network, and types of coding operations at internal nodes, we define three classes of networks, namely, dedicated, flexible, and linear networks. For each class, we propose an achievable coding scheme, analyze its coding delay, and also, compare it with an information theoretic lower bound. For flexible networks, we show that our scheme is order-optimal in terms of coding delay and, interestingly, the optimal memory-delay curve is achieved in certain regimes. In general, our results suggest that, in case of networks with multiple servers, type of network topology can be exploited to reduce service delay.