By offloading the computation tasks of the mobile devices (MDs) to the edge server, mobile-edge computing (MEC) provides a new paradigm to meet the increasing computation demands from mobile applications. However, existing mobile-edge computation offloading (MECO) research only took the resource allocation between the MDs and the MEC servers into consideration, and ignored the huge computation resources in the centralized cloud computing center. Moreover, current MEC hosted networks mostly adopt the networking technology integrating cellular and backbone networks, which have the shortcomings of single access mode, high congestion, high latency, and high energy consumption. Toward this end, we introduce hybrid fiber-wireless (FiWi) networks to provide supports for the coexistence of centralized cloud and multiaccess edge computing, and present an architecture by adopting the FiWi access networks. The problem of cloud-MEC collaborative computation offloading is studied, and two schemes are proposed as our solutions, i.e., an approximation collaborative computation offloading scheme, and a game-theoretic collaborative computation offloading scheme. Numerical results corroborate that our solutions not only achieve better offloading performance than the available MECO schemes but also scale well with the increasing number of computation tasks.