Data cube computation is one of the most essential but expensive operations in data warehousing. Previous studies have developed two major approaches, top-down vs. bottomup. The former, represented by the Multi-Way Array Cube (called MultiWay) algorithm , aggregates simultaneously on multiple dimensions; however, it cannot take advantage of Apriori pruning  when computing iceberg cubes (cubes that contain only aggregate cells whose measure value satisfies a threshold, called iceberg condition). The latter, represented by two algorithms: BUC  and H-Cubing, computes the iceberg cube bottom-up and facilitates Apriori pruning. BUC explores fast sorting and partitioning techniques; whereas H-Cubing explores a data structure, H-Tree, for shared computation. However, none of them fully explores multi-dimensional simultaneous aggregation. In this paper, we present a new method, Star-Cubing, that integrates the strengths of the previous three algorithms and performs aggregations on multiple dimensions simultaneously. It utilizes a star-tree structure, extends the simultaneous aggregation methods, and enables the pruning of the group-by's that do not satisfy the iceberg condition. Our performance study shows that Star-Cubing is highly efficient and outperforms all the previous methods in almost all kinds of data distributions.