For the system of equations:

$$\left\{\begin{aligned}&x^2+y^2+z^2=u^2+w^2+v^2\\&x+y+v=u+w+z\end{aligned}\right.$$

You can record solutions:

$$x=s^2+kt-ks+kq+ts-tq-qs$$

$$y=s^2+kt+ks-kq-ts+tq-qs$$

$$z=s^2+kt+ks-kq+ts-tq+2q^2-3qs$$

$$u=s^2+kt+ks-kq+ts-tq-qs$$

$$w=kt-s^2-ks+kq-ts+tq-2q^2+3qs$$

$$v=kt-s^2+ks-kq+ts-tq+qs$$

$s,q,k,t$ - integers asked us.