2026 IMC keystage3-IWYMIC individual Question 4

Let $a,b,c$ be non-negative real numbers. Define $X=(2a+b+c)(b+c)+c^2$, $Y=(a+2b+c)(a+c)+a^2$, $Z=(a+b+2c)(a+b)+b^2$. If $X+Y+Z=12$, find $(a^3+b^3+c^3-8)/[(2-a)(2-b)(2-c)]$.