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Facing a vast amount of connections, huge performance demands, and the need for reliable connectivity, the sixth generation of communication networks (6G) is envisioned to implement disruptive technologies that jointly spur connectivity, performance, and reliability. In this context, this paper proposes, and evaluates the benefit of, a hybrid central cloud (CC) computing and mobile edge computing (MEC) platform, especially introduced to balance the network resources required for joint computation and communication. Consider a hybrid cloud and MEC system, where several power-hungry multi-antenna unmanned aerial vehicles (UAVs) are deployed at the cell-edge to boost the CC connectivity and relieve part of its computation burden. While the multi-antenna base stations are connected to the cloud via capacity-limited fronthaul links, the UAVs serve the cell-edge users with limited power and computational capabilities. The paper then considers the problem of maximizing the weighted network sum-rate subject to per-user delay, computational capacity, and power constraints, so as to determine the beamforming vectors and computation allocations. Such intricate non-convex optimization problem is tackled using an iterative algorithm that relies on $\ell_0$-norm relaxation, successive convex approximation, and fractional programming, and has the compelling ability to be implemented in a distributed fashion across the multiple UAVs and the CC. The paper results illustrate the numerical prospects of the proposed algorithm for enabling joint communication and computation, and highlight the appreciable improvements of data processing delays and throughputs as compared to conventional system strategies.