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 the specified query ranges. The direct method to access the data cube itself forces too many cells to be accessed, therefore it incurs a severe overhead. The response time is very crucial for OLAP applications which need interactions with users. In the recent dynamic enterprise environment, data elements in the cube are frequently changed. The response time is affected in such an environment by the update cost as well as the search cost of the cube. In this paper, we propose an efficient algorithm to reduce the update cost significantly while maintaining reasonable search efficiency, by using an index structure called the ∆-tree. In addition, we propose a hybrid method to provide either an approximate result or a precise one to reduce the o...