Just as the title, prove $(\oplus_{n=1}^{\infty}\ell_1^n)_{\ell_2}$ cannot admit a norm which is uniformly convex.
I find in the answer of A reflexive space which does not have an equivalent uniformly convex norm , a user noticed using Enflo's theorem, but he did not mention what this theorem says, and I cannot find a version of this theorem on the internet.