Write the value of $\left(x^3-y^3-z^3-3xyz\right)$  if $x=y+z$.

Prove that $x^3+y^3+3m=\frac{m^3}{x^3{y}^3}$ if $xy\left(x+y\right)=m$.

Prove that $27x^3+\frac{1}{8x^3}=189$ if $2x+\frac{1}{3x}=4$.

Find the value of $a^3-\frac{1}{a^3}+2$ if $2a-\frac{2}{a}+1=0$.

Find the value of $\left(a+b+c\right)$ by calculation if $a^3+b^3+c^3=3abc (a\ne b\ne c)$.

Write the value of $\left(m^2+n^2\right)\left(m^3+n^3\right)$ by calculation if $m+n=5$ and $mn=6$.

If $\left(7+3x\right)\left(49-21x+9x^2\right)=343+k{x}^3$, then find the value of $k$.

If the product of $\left(x^2+y^2\right)\left(x^4-x^2{y}^2+y^4\right)$ is equal to $x^6+y^k$, then find the value of $k$.

Factorize the following:

$x^3+125$