The emerging cloud computing paradigm enables cloud systems to provide multiple heterogeneous types of cloud resources for end customers over a network. Users and providers in these systems attempt to maximize their revenue using well-designed pricing methods. Auctions are considered as efficient mechanisms for resource sharing and charging users in cloud systems. We study the online social welfare maximization problem at a cloud market, and design efficient pricing functions to be used in online auction mechanisms for cloud resource provisioning, for tasks with completion deadlines. Combining the techniques of primal-dual approximation algorithm design with our proposed pricing methods, we design a cloud auction that runs efficiently in polynomial time, guarantees truthfulness, and achieves near-optimal social welfare, in the cloud eco-system. Simulation studies con rm the efficacy of the proposed mechanism.