In this paper we have presented a parallel multidimensional database infrastructure for OLAP and data mining of association rules which can handle a large number of dimensions and large data sets. Parallel techniques are described to partition and load data into a base cube from which the data cube is calculated. Optimizations performed on the cube lattice for construction of the complete and partial data cubes are presented. Our implementation can handle large data sets and a large number of dimensions by using sparse chunked storage using a novel data structure called BESS. Experimental results on data sets with around 3.5 million tuples and having 20 dimensions on a 16 node shared-nothing parallel computer (IBM SP2) show that our techniques provide high performance and are scalable.