Techniques are described herein for efficiently evaluating database queries that include hierarchical cube computations. During second and subsequent evaluation phases (if any), a database server does not re-determine groups (nor re-aggregate within such groups) that have already been determined in a previous evaluation phase. Instead, according to a technique described herein, whenever an evaluation phase subsequent to the first evaluation phase is performed, the database server immediately outputs or otherwise returns certain groups and aggregate results that were determined based on certain grouping column sets that were generated in the previous evaluation phase. The database server does not aggregate within these certain groups when performing aggregation in the current evaluation phase, thereby avoiding the duplication of work already performed during previous evaluation phases.