By a parametrisation of the solutions of the equation $x_1x_2x_3=t^3,\qquad (x_1,x_2,x_3,t)=1$ and by elementary methods of analytic number theory, we show that the number of points, with non–zero coordinates, with canonical height less than $X$, of the cubic projective surface of ${\mathbb P}_3 ({\mathbb Q})$ defined by the equation $X_1X_2X_3=T^3,$ is, for $X\longrightarrow \infty $, asymptotically equivalent to $c_0X \log ^6 X$,where $c_0$ is some positive constant.