If $\sin \theta +\cos \theta =p$ and ${\sin }^3\theta +{\cos }^3\theta =q$, then $p(p^2-3)=$

$\cos \theta +\sin \theta =p\Rightarrow p^2$$=1+2\sin \theta \cos \theta \Rightarrow \sin \theta \cos \theta =\frac{p^2-1}{2}$ also

$p^3={\cos }^3\theta +{\sin }^3\theta +3\cos \theta \sin \theta (\cos \theta +\sin \theta )\Rightarrow p^3=q+3\left(\frac{{\displaystyle p^2-1}}{{\displaystyle 2}}\right)p$

$\Rightarrow 2p^3=2q+3p^3-3p\Rightarrow p^3-3p=-2q$