In the face of expanding digital landscapes, cloud-edge computing infrastructures struggle with an ever-increasing demand for real-time data management. This demand has a direct impact on the energy consumption of cloud-edge networks, which has spiked dramatically, stressing the need for accurate time-series forecasting. As conventional machine learning models encounter difficulties in predicting volatile workloads, attention mechanisms have emerged thanks to their capability of capturing long-range dependencies. This article pioneers the exploration of attention mechanisms for time-series forecasting in cloud-edge environments, particularly focusing on a promising low-complexity attention mechanism (i.e., informer model). Through comprehensive discussions and experimental validations, we demonstrate that informers significantly outperform traditional models in the prediction accuracy of compute workload forecasting. The outcome of this work not only highlights the importance of attention mechanisms in cloud-edge scenarios but also pave the way for future optimizations, ultimately aiming at reducing the environmental impact of digital growth.