In a smart city environment, Data Centers (DCs) play a fundamental role, since they enable urban applications by processing big data which comes from interconnected systems. These processing demands have led to a tremendous increase in DC power consumption. Therefore, the concepts of DC energy efficiency and sustainability represent future challenges in smart cities. While assessment of DC energy efficiency with a set of globally recognized metrics is being currently explored, the area of productivity metrics is not thoroughly studied. In particular, there is no general consensus on metrics for direct evaluation of energy used for productive computing operations, or useful work, in a DC. This chapter proposes methodologies for energy efficiency evaluation of DCs using appropriate energy and productivity metrics, namely Energy Waste Ratio (EWR) and Data Center energy Productivity (DCeP) and discusses sustainability requirements in the smart city context. By exploiting the available dataset recorded in ENEA DC, the authors evaluate energy productivity at different granularity levels: individual jobs, queues and DC cluster. Specifically, portions of energy used for productive computing and energy wasted during computational work are examined. The chapter also provides insights into sustainability of the cluster and proposes a new metric, Carbon Waste Ratio.