7. Given the function $f(x)=\left(\mathrm{e}^{x}-\mathrm{e}^{-x}\right) \cdot x^{3}$, if $m$ satisfies $f\left(\log _{2} m\right)+f\left(\log _{0.5} m\right) \leqslant 2\left(\frac{\mathrm{e}^{2}-1}{\mathrm{e}}\right)$, then the range of real number $m$ is $\qquad$ .
Since the function $f(x)$ is an even function and is monotonically increasing on $(0,+\infty)$, we have $f\left(\log _{2} m\right) \leqslant \frac{\mathrm{e}^{2}-1}{\mathrm{e}}=\mathrm{e}-\mathrm{e}^{-1}=f(1)$ $\Rightarrow\left|\log _{2} m\right| \leqslant 1 \Rightarrow \frac{1}{2} \leqslant m \leqslant 2$. Therefore, $m \in\left[\frac{1}{2}, 2\right]$.