The Interference Channels (ICs) represent fundamental building blocks of wireless communication networks. Despite considerable progress in network information theory, available capacity results for ICs, specifically those with more than two users, are still very limited. One of the main difficulties in the analysis of these networks is how to establish useful capacity outer bounds for them. In this paper, novel techniques requiring subtle sequential application of Csiszar-Korner identity are developed to establish efficient single-letter outer bounds on the sum-rate capacity of interference networks. By using the outer bounds, a full characterization of the sum-rate capacity is then derived for various multi-user ICs under specific conditions. Our capacity results hold for both discrete and Gaussian networks.