Data centers play a pivotal role in modern Internet and cloud computing systems, yet their escalating energy needs present formidable hurdles. Precise energy consumption forecasts are indispensable for optimizing resource allocation. Despite numerous methods proposed, a gap persists in rigorously tackling this issue. Existing approaches often falter in capturing the intricate and stochastic energy consumption patterns, necessitating more comprehensive methodologies. The suggested approach pioneers a novel method for predicting energy usage in cloud data centers, emphasizing the incorporation of random uncertainty. Recognizing this uncertainty is vital due to the variability inherent in factors impacting energy consumption, such as workload fluctuations and hardware failures. By employing regression distributions to model random uncertainty, the methodology aims to more effectively encapsulate the statistical characteristics of energy consumption compared to conventional deterministic models. Rather than furnishing deterministic forecasts, the methodology conceptualizes energy consumption predictions as random variables drawn from regression-derived distributions. This probabilistic paradigm acknowledges and quantifies the inherent uncertainty in energy consumption predictions. Moreover, it extends beyond individual data centers, providing probabilistic forecasts for diverse data center portfolios, accommodating varied configurations and workloads. The methodology introduces several pivotal methodological innovations to enhance prediction accuracy. It proposes a naive multiple linear regression model as a baseline for capturing fundamental relationships. Additionally, it presents a pioneering approach that combines quantile regression and empirical copulas to estimate joint distributions of random variables, capturing complex interdependencies among energy consumption variables. Finally, a weighted correction method, grounded in constrained quantile regression, is introduced to refine predictive distributions, further bolstering accuracy. In conclusion, the methodology addresses the critical challenge of energy consumption prediction in data c\e\nters by embracing the stochastic nature of energy usage. Through rigorous statistical modeling and innovative techniques, it represents a substantial advancement, fostering a nuanced comprehension of energy consumption dynamics and facilitating informed and efficient management strategies.