  In this paper, we introduce a novel algorithm for calculating arbitrary order
cumulants of multidimensional data. Since the $d^\text{th}$ order cumulant can
be presented in the form of an $d$-dimensional tensor, the algorithm is
presented using tensor operations. The algorithm provided in the paper takes
advantage of super-symmetry of cumulant and moment tensors. We show that the
proposed algorithm considerably reduces the computational complexity and the
computational memory requirement of cumulant calculation as compared with
existing algorithms. For the sizes of interest, the reduction is of the order
of $d!$ compared to the naive algorithm.
