Comparison of Some Distances Between Sums of $\ell^{p}_n$ Spaces

In this paper, we study the classical, modified, and weak Banach–Mazur distances between sums of $\ell^p_n$ spaces. We explicitly calculate the classical and weak Banach–Mazur distances between sums of $\ell^p_n$ spaces and establish bounds for the ratios of these distances.