The Cloud Computing paradigm consists in providing customers with virtual services of the quality which meets customers’ requirements. The efficiency of infrastructure exploitation may be expressed by the electrical energy consumption of computing centers, amongst others. We propose to model the energy consumption of private Clouds by a variant of the Bin Packing problem which we analyze next from a theoretical point of view. We advance on-line and off-line approximation algorithms to solve our problem to balance the load either on-the-fly or at the planning stage. In addition to the computation of the approximation factors of these two algorithms, we evaluate their performance experimentally. The quality of the results is encouraging, which makes a packing approach a serious candidate to model energy-aware load balancing in Cloud Computing.