Representation of positive integers by the form $x^3+y^3+z^3-3xyz$

We study the number $\nu (n)$ of representations of a positive integer $n$ by the form $x^3+y^3+z^3-3xyz$ in the conditions $0\le x\le y\le z;z\ge x+1.$ We proved the following results: (i) for every positive $n,$ except for $n\equiv \pm 3(\mathrm{m}\mathrm{o}\mathrm{d}9),$ $\nu (n)>=1;$ (ii) for the exceptional $n,$ $\nu (n)=0;$ (iii) for every prime $p\mathrm{\ne }3,$ $\nu (p)=\nu (2p)=1;$ (iv) $\limsup (\nu(n))=\infty;$(v)foreverypositive$n,$thereexists$k$suchthat$\nu(k)=n.$