The transition from 5G to 6G networks is driving an unprecedented densification of Radio Access Networks (RANs), resulting in increased energy demand and operational costs. Open RAN (O-RAN) architectures, which disaggregate baseband processing across commercial off-the-shelf (COTS) servers, further amplify these challenges due to the power sensitivity of the Distributed Unit (O-DU) to traffic load variations. This paper develops a nonlinear O-DU power model that captures load-dependent efficiency effects and integrates it into a dynamic core management framework, which activates or deactivates CPU cores based on instantaneous traffic demand. The effectiveness of the proposed dynamic core management framework is investigated in multi-RU O-RAN scenarios, comparing the proposed dynamic approach with a static baseline. Simulation results show that the dynamic scheme reduces energy consumption by up to $59.42\%$ on average under light traffic, with instantaneous savings exceeding $70\%$ during off-peak periods, while maintaining performance. These findings demonstrate that workload-aware core provisioning can deliver substantial energy efficiency gains in O-RAN deployments, particularly in lightly to moderately loaded networks.