Both the training and use of Large Language Models (LLMs) require large amounts of energy. Their increasing popularity, therefore, raises critical concerns regarding the energy efficiency and sustainability of data centers that host them. This paper addresses the challenge of reducing energy consumption in data centers running LLMs. We propose a hybrid data center model that uses a cost-based scheduling framework to dynamically allocate LLM tasks across hardware accelerators that differ in their energy efficiencies and computational capabilities. Specifically, our workload-aware strategy determines whether tasks are processed on energy-efficient processors or high-performance GPUs based on the number of input and output tokens in a query. Our analysis of a representative LLM dataset, finds that this hybrid strategy can reduce CPU+GPU energy consumption by 7.5% compared to a workload-unaware baseline.