In this paper, we focus on a large-scale ICN (Information-Centric Networking), and reveal the scaling property of ICN. Because of in-network content caching, ICN is a sort of cache networks and expected to be a promising architecture for replacing future Internet. To realize a global-scale (e.g., Internet-scale) ICN, it is crucial to understand the fundamental properties of such large-scale cache networks. However, the scaling property of ICN has not been well understood due to the lack of theoretical foundations and analysis methodologies. For answering research questions regarding the scaling property of ICN, we derive the cache hit probability at each router, the average content delivery delay of each entity, and the average content delivery delay of all entities over a content distribution tree comprised of a single repository (i.e., content provider), multiple routers, and multiple entities (i.e., content consumers). Through several numerical examples, we investigate the effect of the topology and the size of the content distribution tree and the cache size at routers on the average content delivery delay of all entities. Our findings include that the average content delivery delay of ICNs converges to a constant value if the cache size of routers are not small, which implies high scalability of ICNs, and that even when the network size would grow indefinitely, the average content delivery delay is upper-bounded by a constant value if routers in the network are provided with a fair amount of content caches.