Using a suitable identity,evaluate the following:
$103^{3}$

State whether the following statement is True or False. Justify your answer.
$\frac{6 \sqrt{x} + x^{\frac{3}{2}}}{\sqrt{x}}$ is a polynomial,where $x \neq 0$.

Factorise the following expression: $8x^3 + 343y^3 + 84x^2y + 294xy^2$.

Expand the following:
$(3a - 2b)^3$

If $a+b+c=9$ and $ab+bc+ca=26$,find $a^{2}+b^{2}+c^{2}$.

Expand the following:
$\left(\frac{1}{x}+\frac{y}{3}\right)^{3}$