The growing environmental and sustainability concerns have made energy efficiency a pressing issue for data center operation. Governments, as well as various organizations, are urging data centers to cap the increasing energy consumption. Naturally, achieving long term energy capping involves deciding energy usage over a long timescale (without accurately foreseeing the far future) and hence, we call this process “energy budgeting”. In this paper, we introduce an online resource management solution, called eBud (energy Budgeting), for a virtualized data center. eBud determines the number of servers, resource allocation to virtual machines and corresponding workload distribution to minimize data center operational cost while satisfying a long term energy cap. We prove that eBud achieves a close-to-minimum cost compared to the optimal offline algorithm with future information, while bounding the potential violation of energy budget constraint, in an almost arbitrarily random environment. We also perform a trace-based simulation study to complement the performance analysis. The simulation results show that eBud reduces the cost by more than $\mathrm{16}$ percent (compared to state-of-the-art prediction-based algorithm) while resulting in a zero energy budget deficit. We also perform an experimental study based on RUBiS, demonstrating that in a real life scenario, eBud can achieve energy capping with a negligible increase in operational cost.