Content delivery networks (CDNs) are an important class of Internet-scale distributed systems that deliver web, streaming, and application content to end users. A commercial CDN could comprise hundreds of thousands of servers deployed in over thousand clusters across the globe and incurs significant energy costs for powering and cooling their servers. Since energy costs are a significant component of the total operating expense of a CDN, we propose and explore a novel technique called cluster shutdown that turns off an entire cluster of servers of a CDN that is deployed within a data center. By doing so, cluster shutdown saves not just the power consumed by the servers but also the power needed for cooling those servers. We present an algorithm for cluster shutdown that is based on realistic power models for servers and cooling equipment and can be implemented as a part of the global load balancer of a CDN. We evaluate our technique using extensive real-world traces from a large commercial CDN to show that cluster shutdown can reduce the system-wide energy usage by 67%. Further, much of the energy savings are obtainable without sacrificing either bandwidth costs or end-user performance. In addition, 79% of the optimal savings are attainable even if each cluster is limited to at most one shutdown per day, reducing the required operational overhead. Finally, we argue that cluster shutdown has intrinsic architectural advantages over the well-studied server shutdown techniques in the CDN context, and show that it saves more energy than server shutdown in a wide range of operating regimes.