C (gcc), 85 8181 75 bytes
Saved 4 bytes and then 6 bytes thanks to @ceilingcat@ceilingcat's re-ordering of assignments
r[5];f(n){r[1]=(n=(n-(*r=n*n*n))/6+1)*n*n--;r[2]=;r[3]=r[4]=-n*n*n;r[2]=-n*n*n;r[3]=n=-++n*n*n;r[4]=n;n*n*n;}