The Chain Rule & Implicit Differentiation · Challenge problem

A smooth function $f(x,y)$ is homogeneous of degree $3$, meaning $f(\lambda x, \lambda y) = \lambda^3 f(x,y)$ for all $\lambda > 0$. Given that $f(2, 1) = 5$, find $x^2 f_{xx} + 2xy f_{xy} + y^2 f_{yy}$ at $(2, 1)$.