  In this article we study the stability problem for the Einstein metrics on
Sasaki Einstein and on complete nearly parallel ${\rm G}_2$ manifolds. In the
Sasaki case we show linear instability if the second Betti number is positive.
Similarly we prove that nearly parallel $\rm G_2$ manifolds with positive third
Betti number are linearly unstable. Moreover, we prove linear instability for
the Berger space ${\rm SO}(5)/{\rm SO}(3)_{irr} $ which is a $7$-dimensional
homology sphere with a proper nearly parallel ${\rm G}_2$ structure.
