SUM queries are crucial for many applications that need to deal with uncertain data. In this paper, we are interested in the queries, called ALL_SUM, that return all possible sum values and their probabilities. In general, there is no efficient solution for the problem of evaluating ALL_SUM queries. But, for many practical applications, where aggregate values are small integers or real numbers with small precision, it is possible to develop efficient solutions. In this paper, based on a recursive approach, we propose a new solution for this problem. We implemented our solution and conducted an extensive experimental evaluation over synthetic and real-world data sets; the results show its effectiveness.