The underlying infrastructure of cloud computing relies on data centers monitored and maintained by the cloud service providers. Data centers usually incur enormous power consumption and are expected to have a significant impact on the local power grid due to dramatically increasing power consumption and fluctuation. In order to mitigate such fluctuation and balance the power demand and supply in the power grid in real time, the regulation service (RS) opportunity has been provided, which offers the electricity consumers to dynamically adjust their power consumption and reduce their electricity cost. Data centers can be active RS participants due to their flexibility and controllability in load dispatching and scheduling temporally (within a server) and spatially (among multiple servers). In order for the data centers to provide better RS, prediction on the data center power consumption becomes essential. In this work, we first adopt artificial neural network (ANN)-based method and long short term memory (LSTM) neural network-based method for the prediction of future data center power consumption. Based on the prediction results, we formulate a novel optimal power management problem of data center to minimize the total cost. Experimental results demonstrate that the total cost of the data center can be reduced by up to 20.6% compared with the baseline systems.