Multidimensional aggregation is a dominant operation on data warehouses for on-line analytical processing (CLAP). Many efficient algorithms to compute multidimensional aggregation on relational database based data warehouses have been developed. However, to our knowledge, there is nothing to date in the literature about aggregation algorithms on multidimensional data warehouses that store datasets in multidimensional arrays rather than in tables. This paper presents a set of multidimensional aggregation algorithms on very large and compressed multidimensional data warehouses. These algorithms operate directly on compressed datasets in multidimensional data warehouses without the need to first decompress them. They are applicable to a variety of data compression methods. The algorithms have different performance behavior as a function of dataset parameters, sizes of outputs and main memory availability. The algorithms are described and analyzed with respect to the I/O and CPU costs. A decision procedure to select the most efficient algorithm, given an aggregation request, is also proposed. The analytical and experimental results show that the algorithms are more efficient than the traditional aggregation algorithms.