Starting from a positive integer $n$, at each step we subtract from $n$ the largest perfect cube not exceeding $n$, until $n$ becomes $0$.
For example, with $n=100$ the procedure ends in $4$ steps: $$100\stackrel{-4^3}{\to }36\stackrel{-3^3}{\to }9\stackrel{-2^3}{\to }1\stackrel{-1^3}{\to }0.$$ Let $D(n)$ denote the number of steps of the procedure. Thus $D(100)=4$.

Let $S(N)$ denote the sum of $D(n)$ for all positive integers $n$ strictly less than $N$.
For example, $S(100)=512$.

Find $S({10}^{17})$.