A range-sum query is very popular and becomes important in finding trends and in discovering relationships between attributes in diverse database applications. It sums over the selected cells of an OLAP data cube where target cells are decided by specified query ranges. The direct method to access the data cube itself forces too many cells to be accessed, therefore it incurs severe overheads. The prefix-sum cube was proposed for the efficient processing of range-sum queries in OLAP environments. However, the prefix-sum cube has been criticized due to its space requirement. In this paper, we propose a lossless compression method called the overlapped-subcube that is developed for the purpose of compressing prefix-sum cubes. A distinguished feature of the overlapped-subcube is that searches can be done without decompressing. The overlapped-subcube reduces the space requirement for storing prefix-sum cubes, and improves the query performance.