This is easy for $r=2$. For $r=3$ it is not even known if those integers which are the sum of at most three cubes has density $0$.

It does not seem to even be known if all large integers are the sum of at most $r$ many $r$-powerful numbers (in [Er76d] Erdős claims this follows from a simple counting argument, but Schinzel pointed out he made a mistake).

Heath-Brown [He88] has proved that all large numbers are the sum of at most three $2$-powerful numbers.