In this paper, for the first time, a cost efficient network slicing method is proposed for torus data centers based on optical packet switching transport. The torus optical packet switched rings are separately synchronized so that electronic regrooming is employed at the nodes connecting different rings, for the inter-ring transit of optical packet traffic. In the proposed network slicing method called “HYB-BOSS network slicing”, we introduce optical circuit switching over “network slicing paths” in order to leverage low-cost network operation. The resulting network has a hybrid optical packet/circuit switching architecture. Next, an optimal network planning tool is developed to evaluate the cost efficiency of HYB-BOSS network slicing in terms of required optical interfaces and optical fibers when compared with network slicing in purely optical packet switched torus. The numerical results show that HYB-BOSS network slicing can reduce the number of optical interfaces in a network by up to 33%.