In this paper, we introduce and solve the following generalized Drygas functional equation $$ f(x+ky)+f(x-ky)=2f(x)+k^{2}f(y)+k^{2}f(-y), $$ where $k\in \mathbb{N}$. Also, we discuss some stability and hyperstability results for the considered equation in $2$-Banach spaces by using the fixed point approach.