With the rapid proliferation of smart mobile devices and increasing adoption of cloud computing services, energy efficiency has become an important issue in mobile cloud environments. High energy consumption not only results in higher operational costs but also creates sustainability concerns related to cloud infrastructure and services. This paper proposes leveraging big data techniques such as machine learning and predictive analytics to optimize resource allocation and reduce energy consumption in mobile cloud computing. The massive amount of data on factors like user behavior, mobility patterns, network availability, and resource utilization can provide key insights to improve energy efficiency. We present an intelligent predictive framework to forecast mobile cloud resource demands and enable dynamic scaling of cloud configurations aligned to current needs. By proactively adapting cloud resources based on learned models and detected usage patterns, over-provisioning and under-utilization can be minimized. Specifically, we demonstrate how clustering, classification, regression, and times series models derived from contextual usage data can significantly improve energy efficiency when integrated with mobile cloud management systems. The proposed approaches are validated experimentally using simulated workloads and real-world trajectory data sets. Results indicate average energy savings of 42% and up to 62% for certain user groups compared to conventional cloud resource allocation techniques. This work provides an important contribution toward building more sustainable and energy efficient mobile cloud computing systems to meet the mobility and computing demands of the future through the transformative power of big data analytics.