The current paradigm of content distribution networks (CDN) deployment requires heavy infrastructure investment since a large number of servers have to be deployed over a wide area. To overcome this difficulty, we propose a new paradigm where future CDNs are to be deployed over a leased server infrastructure. This paradigm shift changes the object placement problem in current CDNs to a combined object placement and resource provisioning problem. In this paper, we present a formulation of this problem, which is a combinatorial optimization, and prove its NP-hardness. We also present a heuristic solution to this problem based on Lagrangian relaxation and subgradient optimization, which also provides error bounds so that the accuracy of the obtained solution can be evaluated. The algorithm has been implemented and tested on a number of randomly generated network topologies, and results have shown promising solution accuracy.