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We study the number $\nu(n)$ of representations of a positive integer $n$ bythe form $x^3+y^3+z^3-3xyz$ in the conditions $0\leq x\leq y\leq z; z\geq x+1.$We proved the following results: (i) for every positive $n,$ except for$n\equiv\pm3 \pmod9,$ $\nu(n)>=1;$ (ii) for the exceptional $n,$ $\nu(n)=0;$(iii) for every prime $p\neq3,$ $\nu(p)=\nu(2p)=1;$ (iv) $\limsup(\nu(n))=\infty;$ (v) for every positive $n,$ there exists $k$ such that$\nu(k)=n.$

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