Answer
Homogeneous with degree 3
Work Step by Step
Recall that the definition of a homogeneous function is a function that satisfies the following condition
$f(tx,ty)=t^nf(x,y)$ where $n$ is the degree.
If $f(x,y)=x^3-4xy^2+y^3$
all we have to do is plug in the point $(tx,ty)$
$f(tx,ty)=(tx)^3-4(tx)(ty)^2+(ty)^3$
$=t^3x^3-4t^3xy^2+t^3y^3$
$=t^3(x^3-4xy^2+y^3)=t^3f(x,y)$
So the function is homogeneous with a degree of 3
