Power management in multi-server data centers especially at scale is a vital issue of increasing importance in cloud computing paradigm. Existing studies mostly consider thresholds on the number of idle servers to switch the servers on or off and suffer from scalability issues. As a natural approach in view of the Markovian assumption, we present a multi-level continuous-time Markov decision process (CTMDP) model based on state aggregation of multi-server data centers with setup times that interestingly overcomes the inherent intractability of traditional MDP approaches due to their colossal state-action space. The beauty of the presented model is that, while it keeps loyalty to the Markovian behavior, it approximates the calculation of the transition probabilities in a way that keeps the accuracy of the results at a desirable level. Moreover, near-optimal performance is attained at the expense of the increased state-space dimensionality by tuning the number of levels in the multi-level approach. The simulation results were promising and confirm that in many scenarios of interest, the proposed approach attains noticeable improvements, namely a near 50% reduction in the size of CTMDP while yielding better rewards as compared to existing fixed threshold-based policies and aggregation methods.