  Critical fluctuations change the effective anisotropy of cubic ferromagnet
near the Curie point. If the crystal undergoes phase transition into
orthorhombic phase and the initial anisotropy is not too strong, reduced
anisotropy of nonlinear susceptibility acquires at $T_c$ the universal value
$\delta_4^* = {{2v^*} \over {3(u^* + v^*)}}$ where $u^*$ and $v^*$ --
coordinates of the cubic fixed point on the flow diagram of renormalization
group equations. In the paper, the critical value of the reduced anisotropy is
estimated within the pseudo-$\epsilon$ expansion approach. The six-loop
pseudo-$\epsilon$ expansions for $u^*$, $v^*$, and $\delta_4^*$ are derived for
the arbitrary spin dimensionality $n$. For cubic crystals ($n = 3$)
higher-order coefficients of the pseudo-$\epsilon$ expansions obtained turn out
to be so small that use of simple Pad\'e approximants yields reliable numerical
results. Pad\'e resummation of the pseudo-$\epsilon$ series for $u^*$, $v^*$,
and $\delta_4^*$ leads to the estimate $\delta_4^* = 0.079 \pm 0.006$
indicating that detection of the anisotropic critical behavior of cubic
ferromagnets in physical and computer experiments is certainly possible.
