Unmanned aerial vehicles (UAV) have emerged as a practical solution that provides on-demand services to users in areas where the terrestrial network is non-existent or temporarily unavailable, e.g., due to natural disasters or network congestion. In general, UAVs' user-serving capacity is typically constrained by their limited battery life and the finite communication resources that highly impact their performance. This work considers the orthogonal frequency division multiple access (OFDMA) enabled multiple unmanned aerial vehicles (multi-UAV) communication systems to provide on-demand services. The main aim of this work is to derive an efficient technique for the 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 fewer than 10 iterations. The benefits of the proposed design are demonstrated via superior sum-rate performance compared to existing reference designs. Moreover, results showed that the optimal power and sub-carrier allocation help to mitigate the inter-cell interference that directly impacts the system's performance.