  We study the Leibniz $n$-algebra $\textbf{U}_n(\mathfrak{L})$, whose
multiplication is defined via the bracket of a Leibniz algebra $\mathfrak{L}$
as $[x_1,\dots,x_n]=[x_1,[\dots, [x_{n-2},[x_{n-1},x_n]]\dots]]$. We show that
$\textbf{U}_n(\mathfrak{L})$ is simple if and only if $\mathfrak{L}$ is a
simple Lie algebra. An analogue of Levi's theorem for Leibniz algebras in
$\textbf{U}_n(\textbf{Lb})$ is established and it is proven that the Leibniz
$n$-kernel of $\textbf{U}_n(\mathfrak{L})$ for any semisimple Leibniz algebra
$\mathfrak{L}$ is the $n$-algebra $\textbf{U}_n(\mathfrak{L})$.
