This repo contains a C implementation of the algorithm described in the paper On a question of Mordell by Andrew R. Booker and Andrew V. Sutherland
It uses the primesieve and GMP libraries which need to be installed before you can build the software in this repo.
To build just type make.
To search for for solutions to x^3 + y^3 + z^3 = k for cubefree k = +/- 3 mod 9 at most 1000 with |x| > |y| > |z| and |z| <= zmax and d := |x+y| in the interval [2,dmax] with its largest prime divisor p in [pmin,pmax] using n threads running in parallel, type
./zcubes n k pmin pmax dmax zmax
For example
./zcubes 8 57 1 1e9 1e9 1e10
will output 15 solutions for k=57 with d <= 10^9 and |z| <= 10^10 using 8 threads in about 10 seconds (YMMV).