The computation of data cubes usually produces huge outputs. There are two popular methods to solve this problem: Iceberg cube and closed cube, which can be combined together. Due to the importance and usability of closed iceberg cube, how to efficiently compute it becomes a key research issue. A cache-conscious computation method is proposed in this paper. The data are aggregated in a bottom-up manner. In the meantime, the closed cells covering the aggregate cells are discovered and output. Two pruning strategies are used to save unnecessary recursive calls. The Apriori pruning is utilized to support iceberg cube computation. To reduce the number of memory-related stalls and produce the aggregate results efficiently, multiple dimensions are pre-sorted and the software prefetching technology is introduced into data scans. A comprehensive and detailed performance study is conducted on both synthetic data and real data sets. The results show that the proposed closed iceberg cube computation method is efficient and effective.