Data compression is an effective approach to improve the data wharehouses. On line analysis processing (OLAP) is the most important application on the data warehouses, and Cube is one of the most operators in OLAP. Thus, it is a big challenge to develop efficient algorithms for compressed data warehouses. Although many algorithms to compute Cube have been developed recently, there is little to date in the literatures about Cube algorithms for compressed data warehouse. To the authors' knowledge, there is only one paper that presented a Cube algorithm for compressed data warehouses with a special compression method called chunk-offset. A set of Cube algorithms for very large and compressed data warehouses are proposed in this paper. These algorithms operate directly on compressed datasets without the need of decompressing them first. They are applicable to a variety of data compression methods. The datail analysis of I/O and CPU cost are also given, and compared with the existed algorithms by experiment. The analytical and experimental results show that algorithms proposed in this paper are more efficient than other existed ones.