In an IPTV network, video on demand and other video services generate large amount of unicast traffic from video hub office (VHO) to subscribers and, therefore, require additional bandwidth and equipment resources in the network. To reduce this traffic and overall network cost, a portion of the video content (the most popular titles) may be stored in caches closer to subscribers, e.g., in a digital subscriber line access multiplexer (DSLAM), a central office (CO), or in an intermediate office (IO). The problem becomes to minimize cost by optimizing cache memory placement and amount. We present an analytical model of hierarchical cache optimization. This model depends on several basic parameters: traffic volume, cache hit rate as a function of memory size, topology (i.e. number of DSLAMs, service routers at CO, service switches at IO locations), and cost parameters. Some reasonable assumptions about a network cost structure and a hit rate function allow us to obtain an analytically optimal solution for the problem. We then analyze the factors that affect this solution.