  In this paper we prove that the $3$-fold injective tensor product $\ell_1
\widehat{\otimes}_\varepsilon \ell_1 \widehat{\otimes}_\varepsilon \ell_1 $ is
not isomorphic to any subspace of $\ell_1 \widehat{\otimes}_\varepsilon
\ell_1$. This result provides a new solution to a problem of Diestel on the
projective tensor products of $c_0.$ Moreover, this result implies that for any
infinite countable compact space $K,$ the $3$-fold projective tensor product
$C(K) \widehat{\otimes}_\pi C(K)\widehat{\otimes}_\pi C(K)$ is not isomorphic
to any quotient of $C(K) \widehat{\otimes}_\pi C(K)$.
