Theoretical models suggest that social networks influence the evolution of cooperation, but to date there have been few experimental studies. Observational data suggest that a wide variety of behaviors may spread in human social networks, but subjects in such studies can choose to befriend people with similar behaviors, posing difficulty for causal inference. Here, we exploit a seminal set of laboratory experiments that originally showed that voluntary costly punishment can help sustain cooperation. In these experiments, subjects were randomly assigned to a sequence of different groups in order to play a series of single-shot public goods games with strangers; this feature allowed us to draw networks of interactions to explore how cooperative and uncooperative behavior spreads from person to person to person. We show that, in both an ordinary public goods game and in a public goods game with punishment, focal individuals are influenced by fellow group members' contribution behavior in future interactions with other individuals who were not a party to the initial interaction. Furthermore, this influence persists for multiple periods and spreads up to three degrees of separation (from person to person to person to person). The results suggest that each additional contribution a subject makes to the public good in the first period is tripled over the course of the experiment by other subjects who are directly or indirectly influenced to contribute more as a consequence. These are the first results to show experimentally that cooperative behavior cascades in human social networks.