  Fusion reactions induced by the weakly bound nucleus $^{6}$Li with targets
$^{28}$Si, $^{64}$Ni, $^{144}$Sm and $^{209}$Bi at energies around the Coulomb
barrier are investigated within a three-body model where $^{6}$Li is described
with an $\alpha + d$ cluster model. The total fusion (TF) cross sections are
calculated with the continuum-discretized coupled-channel (CDCC) method and the
complete fusion (CF) cross sections are extracted through the sum-rule model.
The calculations demonstrate that (i) for the TF cross section calculations,
the continuum states up to 40 MeV are found to be necessary, which corresponds
to the inclusion of closed channels for light and medium mass targets, such as
$^{28}$Si, $^{59}$Co and $^{144}$Sm, (ii) the converged CDCC results for TF
cross section at energies above the Coulomb barrier are almost the same as
single channel results in which the continuum coupling effect is neglected, and
(iii) the continuum coupling strongly influences partial wave fusion cross
sections and the closed channels play a significant role in the improvement of
the description of the CF cross sections at energies below the Coulomb barrier
for the $^6$Li+$^{28}$Si, $^{59}$Co and $^{144}$Sm systems.
