The performance of sorting algorithms has a great impact on many computationally intensive applications. Researchers worked on parallelizing many sorting algorithms on various interconnection networks to improve their sequential counterpart performance. One of these interconnection networks is the optical chained-cubic tree (OCCT). In this paper, a parallel bucket sort (PBS) algorithm is presented and applied to the OCCT interconnection network. This PBS algorithm is evaluated analytically and by simulation in terms of various performance metrics including parallel runtime, computation time, communication time, concatenation time, speedup, and efficiency, for a different number of processors, dataset sizes, and data distributions including random and descending. Simulation results show that the highest obtained speedup is approximately 912x on OCCT using 1020 processors, which means the parallel runtime of the PBS on 1020 processors is 912 times faster than the sequential runtime of BS on a single processor.