We consider a virtualized data center (VDC) consisting of a set of servers hosting a number of mobile terminals forming a mobile cloud and study the problem of optimal resource allocation in the presence of time varying workloads and uncertain channels. The channel uncertainty may be due to fading and/or uncertain link availability and reliability in cognitive wireless networks. The servers are processing certain applications delegated to them by the terminals, for either energy saving or due to the lack of necessary software at the terminal to process the applications. The control problem is to dynamically adjust resources according to channel and workload fluctuations in order to maximize the long-term average throughput and to minimize the energy cost of the overall system while maintaining network stability. We develop a unified VDC model for both cognitive and conventional wireless networks, carry out a unified stability analysis, and characterize the joint stability region for the unified VDC model. We also propose a new dynamic policy that supports every point in the network stability region, outperforms previously proposed network stabilizing policies without using the information of arrival statistics, and mitigates the mutual impact of primary and secondary service providers on each other.