In data center networks (DCNs), secure multicast provisioning services are obtained from data centers and transported to multiple users in a multicast style, which requires a high demand for security. Moreover, these services are usually stored and maintained in multiple geographically dispersed data centers for more reliable and efficient access. Quantum key distribution (QKD) is a state-of-the-art technology employed to unconditionally distribute security keys, based on the principles of quantum physics. Therefore, one should pay more attention to how to efficiently distribute global quantum keys in quantum DCNs in the near future. We investigate the problem of global QKD while leveraging multicast service backups among multiple geographically distributed datacenters for secure service provisioning. A distributed subkey-relay-tree-based, secure multicast scheme is proposed and used as a basis to develop a distributed subkey-relay-tree-based secure multicast-routing and key assignment algorithm. Numerical results show that the latter can achieve higher security probability and lower consumed keys compared with the traditional routing and key assignment scheme and single-key-relay-tree-based secure multicast scheme.