In this paper, we consider an Unmanned Aerial Vehicle (UAV)-assisted cellular system which consists of multiple UAV base stations (BSs) cooperating the terrestrial BSs. In such a heterogeneous network, for cellular operators, the problem is how to determine the appropriate number, locations, and altitudes of UAV-BSs to improve the system sumrate as well as satisfy the demands of arbitrarily flash crowds on data rates. We propose a data-driven 3D placement of UAV-BSs for providing an effective placement result with a feasible computational cost. The proposed algorithm searches for the appropriate number, location, coverage, and altitude of each UAV-BS in the serving area with the maximized system sumrate in polynomial time so as to guarantee the minimum data rate requirement of UE. The simulation results show that the proposed approach can improve system sumrate in comparison with the case without UAV-BSs.