Weak Amenability of a Class of Banach Algebras We show that, if a Banach algebra $\A$ is a left ideal in its second dual algebra and has a left bounded approximate identity, then the weak amenability of $\A$ implies the ($2m+1$)-weak amenability of $\A$ for all $m\geq 1$. Keywords:$n$-weak amenability, left ideals, left bounded approximate identityCategories:46H20, 46H10, 46H25