  In this paper we define and discuss the representations of $n$-BiHom-Lie
algebra. We also introduce $T_{\theta}$-extensions and
$T_{\theta}^{\ast}$-extensions of $n$-BiHom-Lie algebras and prove the
necessary and sufficient conditions for a $2m$-dimensional quadratic
$n$-Bihom-Lie algebra to be isomorphic to a $T_{\theta}^{\ast}$-extension.
Moreover, we develop the one-parameter formal deformations of $n$-BiHom-Lie
algebras, and we proved that the first and second cohomology groups are
suitable to the deformation theory involving infinitesimals, equivalent
deformations, and rigidity
