Extended affine Lie algebras (EALA) were first introduced by physicists H{\o}egh-Krohn and Torresani, as a generalization of finite-dimensional simple Lie algebras and affine Kac-Moody Lie algebras over the complex numbers $\mathbb{C}$. In 2006, Yoshii gave a simple characterization of the core of an EALA. Namely, he showed that the core of any EALA is a Lie torus, and any centreless Lie torus is the centreless core of some EALA.In this talk, the finite-dimensional irreducible representations of the nullity 2 centreless core $\mathfrak{g}_{2n,\rho} (\mathbb{C}_q)$ will be discussed by investigating the structure of the $\mathrm{BC}_n$-graded Lie algebra $\mathfrak{g}_{2n,\rho}(R)$. This talk is based on the joint work with Sandeep Bhargava and Yun Gao.