  The role of near-neighbor electron attraction $V$ in strongly correlated
systems has been at the forefront of recent research of unconventional
superconductivity. However, its implications in the doped Hubbard model on
expansive systems remain predominantly unexplored. In this study, we employ the
density-matrix renormalization group to examine its effect in the lightly doped
$t$-$t'$-Hubbard model on six-leg square cylinders, where $t$ and $t'$ are the
first and second neighbor electron hopping amplitudes. For positive $t'$ in the
electron-doped case, our results show that the attractive $V$ can significantly
enhance the superconducting correlations and drive the system into a pronounced
superconducting phase when the attraction exceeds a modest value $V_c \approx
0.7t$. In contrast, in the hole-doped regime with negative $t' $, while
heightened superconducting correlations have also been observed in the charge
stripe phase, the systems remain insulating with pronounced charge density wave
order. Our results demonstrate the importance of the electron attraction in
boosting superconductivity in broader doped Hubbard systems and highlight the
asymmetry between the electron and hole-doped regimes.
