2. Given that $f(x)$ is an odd function defined on $\mathbf{R}$, and the function $y=f(x+1)$ is an even function. When $-1 \leqslant x \leqslant 0$, $f(x)=x^{3}$, then $f\left(\frac{9}{2}\right)=$ $\qquad$
$f(x)$ is symmetric about the origin $(0,0)$ and the line $x=1$, and its period is 4, so $f\left(\frac{9}{2}\right)=f\left(\frac{1}{2}\right)=-f\left(-\frac{1}{2}\right)=\frac{1}{8}$.