  In [4], some quasi-Hopf algebras of dimension $n^{3}$, which can be
understood as the quasi-Hopf analogues of Taft algebras, are constructed.
Moreover, the quasi-Hopf analogues of generalized Taft algebras are considered
in [7], where the language of the dual of a quasi-Hopf algebra is used. The
Drinfeld doubles of such quasi-Hopf algebras are computed in this paper. The
authors in [5] shew that the Drinfeld double of a quasi-Hopf algebra of
dimension $n^{3}$ constructed in [4] is always twist equivalent to Lusztig's
small quantum group $u_q(sl_2)$ if $n$ is odd. Based on computations and
analysis, we show that this is \emph{not} the case if $n$ is even. That is, the
quasi-Hopf analogue $Qu_q(sl_2)$ of $u_q(sl_2)$ is gotten.
