This work considers the orthogonal frequency division multiple access (OFDMA) technology that enables multiple unmanned aerial vehicles (multi-UAV) communication systems to provide on-demand services. The main aim of this work is to derive the optimal allocation of radio resources, 3D placement of UAVs, and user association matrices. To achieve the desired objectives, we decoupled the original joint optimization problem into two sub-problems: i) 3D placement and user association and ii) sum-rate maximization for optimal radio resource allocation, which are solved iteratively. The proposed iterative algorithm is shown via numerical results to achieve fast convergence speed after less than 10 iterations. The benefits of the proposed design are demonstrated via superior sum-rate performance compared to existing reference designs. Moreover, the results declared that the optimal power and sub-carrier allocation helped mitigate the co-cell interference that directly impacts the system's performance.