  We argue that the conjectural relation between the subleading term in the
small-squashing expansion of the free energy of general three-dimensional CFTs
on squashed spheres and the stress-tensor three-point charge $t_4$ proposed in
arXiv:1808.02052: $F_{\mathbb{S}^3_{\varepsilon}}^{(3)}(0)=\frac{1}{630}\pi^4
C_{\scriptscriptstyle T} t_4$, holds for an infinite family of holographic
higher-curvature theories. Using holographic calculations for quartic and
quintic Generalized Quasi-topological gravities and general-order
Quasi-topological gravities, we identify an analogous analytic relation between
such term and the charges $t_2$ and $t_4$ valid for five-dimensional theories:
$F_{\mathbb{S}^5_{\varepsilon}}^{(3)}(0)=\frac{2}{15}\pi^6 C_{
\scriptscriptstyle T} \left[1+\frac{3}{40} t_2+\frac{23}{630} t_4\right]$. We
test both conjectures using new analytic and numerical results for
conformally-coupled scalars and free fermions, finding perfect agreement.
