The [heuristic](http://www.jstor.org/stable/2152950) from circle method for integral points on diagonal cubic surfaces $x^3+y^3+z^3=a$ ($a$ is a cubic-free integer) seems to fit well with numerical computations by [ANDREAS-STEPHAN ELSENHANS AND JORG JAHNEL](http://www.ams.org/journals/mcom/2009-78-266/S0025-5718-08-02168-6/S0025-5718-08-02168-6.pdf). The only known exception is the surface $x^3+y^3+z^3=2$. Circle method predicts that the number of integral points $(x,y,z)$ with $\max(\vert x\vert,\vert y \vert,\vert z\vert)<N$ is $\approx 0.16\log N$. But parametric solutions $(1+6t^3,1-6t^3,-6t^2)$ are missing.

**Question:** Why the heuristic fails for $x^3+y^3+z^3=2$?