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Network cache allocation and management are important aspects of an Information-Centric Network (ICN) design, such as one based on Named Data Networking (NDN). We address the problem of optimal cache size allocation and content placement in an ICN in order to maximize the caching gain resulting from routing cost savings. While prior art assumes a given cache size at each network node and focuses on content placement, we study the problem when a global, network-wide cache storage budget is given and we solve for the optimal per-node cache allocation. This problem arises in cloud-based network settings where each network node is virtualized and housed within a cloud data center node with associated dynamic storage resources acquired from the cloud node as needed. As the offline centralized version of the optimal cache allocation problem is NP-hard, we develop a distributed adaptive algorithm that provides an approximate solution within a constant factor from the optimal. Performance evaluation of the algorithm is carried out through extensive simulations over multiple network topologies, demonstrating that our proposal significantly outperforms existing cache allocation algorithms.