  We prove that for a number of ultrahomogeneous structures $M$, including
those with the free amalgamation property, the powers of the automorphism group
${\rm{Aut}}(M)^n$, $n=1,2,\ldots$, and the group $L_0({\rm{ Aut}}(M))$ of
measurable functions with values in ${\rm{Aut}}(M)$, have a cyclically dense
conjugacy class, in particular, are topologically 2-generated. This provides a
number of new examples of groups with this property. Moreover, we will show
that each of these groups is cyclically generated by a pair generating the free
group.
