Energy efficiency is a major issue in Cloud computing infrastructure. The large power consumption is mainly attributed to the large number of modern data centers operating within. Developing these data centers includes dynamically expanding their infrastructures to meet the ever-increasing demand for huge computation, large storage, and massive communication. Energy conservation through optimization of resources and management policies in the Cloud are a viable solution. Using virtualization to save power and employing such practices as using Virtual Machines (VMs), Server Consolidation, and VM Live Migration. This paper investigates the opportunities for Green Cloud Computing (GCC) to obtain a more comprehensive prospect towards achieving energy efficient Cloud Computing, and presents an energy efficient network resources management approach in an Infrastructure as a Service (IaaS) Cloud model. We focus on developing an energy efficient algorithm by proposing a practical multi-level Cloud Resource-Network Management (CRNM) algorithm, which is implemented in a virtual Cloud environment using Snooze framework as the Cloud energy efficiency manager. The optimization focuses on the utilization of network bandwidth as main resource under test, while also taking into account the other resources, such as CPU and memory, to get the desired performance. We choose a fat tree topology as a common three tier architecture for Cloud data canters. We conclude that our proposed algorithm will save up to 75% of power consumption in Cloud data centers, with an observed increase in efficiency compared to Non-Power Aware (NPA), Power aware(PA), and Greedy algorithms, where network elements consume about 30% of the total power of Cloud data centers.