  Let $f$ be a positive definite integral ternary quadratic form and let
$r(k,f)$ be the number of representations of an integer $k$ by $f$. In this
article we study the number of representations of squares by $f$. We say the
genus of $f$, denoted by $\text{gen}(f)$, is indistinguishable by squares if
for any integer $n$, $r(n^2,f)=r(n^2,f')$ for any quadratic form $f' \in
\text{gen}(f)$. We find some non trivial genera of ternary quadratic forms
which are indistinguishable by squares. We also give some relation between
indistinguishable genera by squares and the conjecture given by Cooper and Lam,
and we resolve their conjecture completely.
