We study an energy-efficient unmanned aerial vehicle (UAV) multicast system, in which ground terminals (GTs) requiring a common information (CI) are grouped and a UAV flies to each group to deliver the CI using minimum energy consumption. A machine learning (ML) empowered joint multicast grouping and UAV trajectory optimization framework is proposed to tackle the challenging joint optimization problem. In this framework, we first propose the compressed-feature regression and clustering machine learning (C2ML) for multicast grouping. A support vector regression (SVR) is trained with the silhouette coefficient, a one- dimensional compressed feature regarding the distribution of GTs, to efficiently determine the number of groups that guides the K-means clustering to approach the optimal multicast grouping. With the C2ML- enabled multicast grouping, we solve the UAV trajectory optimization problem by formulating an equivalent centroid-adjustable traveling salesman problem (CA- TSP). An efficient CA-TSP inspired iterative optimization algorithm is proposed for UAV trajectory planning. The proposed ML-empowered joint optimization framework, which integrates the offline C2ML-enabled multicast grouping and the online CA-TSP inspired UAV- trajectory optimization, is shown to achieve excellent energy-saving performance.