If $f\left(x\right)$ is continuous in $\left[a,b\right]$ and differentiable in (a,b), then prove that there exists at least one $c\in \left(a,b\right)$ such that $\frac{f^{prime}\left(c\right)}{3c^2}=\frac{f\left(b\right)-f\left(a\right)}{b^3-a^3}$

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