Enhancing on line analytical processing through efficient cube computation plays a key role in Data Warehouse management. Hashing, grouping and mining techniques are commonly used to improve cube pre-computation. BitCube, a fast cubing method which uses bitmaps as inverted indexes for grouping, is presented. It horizontally partitions data according to the values of one dimension and for each resulting fragment it performs grouping following bottom-up criteria. BitCube allows also partial materialization based on iceberg conditions to treat large datasets for which a full cube pre-computation is too expensive. Space requirement of bitmaps is optimized by applying an adaption of the WAH compression technique. Experimental analysis, on both synthetic and real datasets, shows that BitCube outperforms previous algorithms for full cube computation and results comparable on iceberg cubing.