  We study a perturbative expansion of the squashed 3-sphere ($S^3_b$)
partition function of 3d $\mathcal{N}=2$ gauge theories around the squashing
parameter $b= 1$. Our proposal gives the coefficients of the perturbative
expansion as a finite sum over the saddle points of the
supersymmetric-localization integral in the limit $b \rightarrow 0$ (the
so-called Bethe vacua), and the contribution from each Bethe vacua can be
systematically computed using saddle-point methods. Our expansion provides an
efficient and practical method for computing basic CFT data ($F,C_T,C_{JJ}$ and
higher-point correlation functions of the stress-energy tensor) of the IR
superconformal field theory without performing the localization integrals.
