Sums of squares appear naturally as solutions to polynomial positivity problems via famous Kirvine-Stengle Positivstellensatz. The reach of such methods is however much wider and extends to the non-commutative setting of *-algebras. In particular the positivity of a particular element in group $C^*$-algebra is equivalent to Kazhdan property (T) which is originally defined in the language of unitary group actions on Hilbert spaces. N.~Ozawa showed that the positivity truly holds in the group algebra and that property (T) always follows from the existence of a finite sum of squares decomposition. This result was the base of the new computational method for proving property (T).  We show that such methods can not only be used for single groups but a well-crafted single computation, through a sequence of embeddings, will establish the property for a whole family of groups. With D.~Kielak and P.W.~Nowak we applied this technique to $Aut(F_n)$, the automorphisms of the free group, proving property (T) for $n \geqslant 5$ and hence solving a major problem in geometric group theory. As a byproduct we obtain lower estimates on the Kazhdan constant which are notoriously hard to compute.