The Cloud Computing paradigm consists in providing customers with virtual services of the quality which meets customers' requirements. A cloud service operator is interested in using his infrastructure in the most efficient way while serving customers. The efficiency of infrastructure exploitation may be expressed, amongst others, by the electrical energy consumption of computing centers. We propose to model the energy consumption of private Clouds, which provides virtual computation services, by a variant of the Bin Packing problem. This novel generalization is obtained by introducing such constraints as: variable bin size, cost of packing and the possibility of splitting items. We analyze the packing problem generalization 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 on the planning stage. In addition to the computation of the approximation factors of these two algorithms, we evaluate experimentally their performance. The quality of the results is encouraging. This conclusion makes a packing approach a serious candidate to model energy-aware load balancing in Cloud Computing.