With the rapid growth of Cloud Computing technologies, enterprises are increasingly deploying their services in the Cloud. Dynamically priced cloud resources such as the Amazon EC2 Spot Instance provides an efficient mechanism for cloud service providers to trade resources with potential buyers using an auction mechanism. With the dynamically priced cloud resource markets, cloud consumers can buy resources at a significantly lower cost than statically priced cloud resources such as the on-demand instances in Amazon EC2. While dynamically priced cloud resources enable to maximize datacenter resource utilization and minimize cost for the consumers, unfortunately, such auction mechanisms achieve these benefits only at a cost significant of private information leakage. In an auction-based mechanism, the private information includes information on the demands of the consumers that can lead an attacker to understand the current computing requirements of the consumers and perhaps even allow the inference of the workload patterns of the consumers. In this paper, we propose PADS, a strategy-proof differentially private auction mechanism that allows cloud providers to privately trade resources with cloud consumers in such a way that individual bidding information of the cloud consumers is not exposed by the auction mechanism. We demonstrate that PADS achieves differential privacy and approximate truthfulness guarantees while maintaining good performance in terms of revenue gains and allocation efficiency. We evaluate PADS through extensive simulation experiments that demonstrate that in comparison to traditional auction mechanisms, PADS achieves relatively high revenues for cloud providers while guaranteeing the privacy of the participating consumers.