Until now, the only known integer solutions to the equation $x^{3}+y^{3}+z^{3}=3$ were $(x, y, z)=(1,1,1)$ and $(4, 4, -5)$ (up to their permuations). I have just seen on Facebook someone posting that
$$569936821221962380720^3 + (-569936821113563493509)^3 + (-472715493453327032)^3 = 3,$$ but didn't reveal the discoverer of the result. Also, i couldn't find any news of this on Google. Has anyone else heard of this yet ?