In recent years, more and more people see their work depend on data manipulation tasks. However, many of these users do not have the background in programming required to write complex programs, particularly SQL queries. One way of helping these users is to automatically synthesize the SQL query given a small set of examples provided by the user -a task known as Query Reverse Engineering. In the last decade, a large plethora of program synthesizers for SQL have been proposed, but none of the current tools take advantage of the increased number of cores per processor.This paper proposes Cubes, a parallel program synthesizer for the domain of SQL queries using input-output examples. Cubes extends current sequential query synthesizers with new pruning techniques and a divide-and-conquer approach, splitting the search space into smaller independent sub-problems.Examples are an under-specification, and the synthesized query may not match the user's intent. We improve the accuracy of Cubes by developing a disambiguation procedure based on fuzzing that interacts with the user and increases our confidence that the returned query matches the user intent.We perform an extensive evaluation on around 4000 SQL queries from different domains. Experimental results show that our sequential version can solve more instances than other state-of-the-art SQL synthesizers. Moreover, the parallel approach can scale up to 16 processes with super-linear speedups for many hard instances. Our disambiguation approach is critical to achieving an accuracy of around 75%, significantly larger than other SQL synthesizers.