Compare with standard masters theorem,
$T(n)=aT(n/b)+\Theta( f(n))$
So given problem is,
$T(n)=16T(n/4)+ \Theta(n^{3})$
So, a=16, b=4.
So, $n^{\log_{b}a}=n^{\log_{4}16}=n^{2}$
So , It is the case 3 of the masters theorem where ,
$f(n)=\Omega (n^{\log_{b}a +\epsilon })$ and it holds regularity condition so ,
$T(n)=\Theta(f(n))=\Theta(n^{3})$.