Algebraic Identities

Study the given statements
Statement-$\mathrm{I}$:
$\frac{{\left(a^2-b^2\right)}^3+{\left(b^2-c^2\right)}^3+{\left(c^2-a^2\right)}^3}{{\left(a+b\right)}^3+{\left(c+a\right)}^3+{\left(a+c\right)}^3}=\left(a+b\right)\left(b+c\right)\left(c+a\right)$
Statement-$\mathrm{II}$:
$a^2+b^2+c^2-ab-bc-ca$
$=\frac{1}{2}{\left[\right(a-b)}^2+{(b-c)}^2+{(c-a)}^2$
Which of the following option holds?

If $a,b,c$ are all non-zeroes and $a+b+c=0$ then $\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}=$_____

The value of ${(x-a)}^3{+(x-b)}^3{+(x-c)}^3-3\left(x-a\right)\left(x-b\right)(x-c)$ when $a+b+c=3x$

The product of $\left(a+b\right)\left(a-b\right)(a^2-ab+b^2)$ $(a^2+ab+b^2)$ is equal to _________