Factorization of  $1029-3x^3$ is $3(k-x)\left(49+kx+x^2\right)$. Then find the value of k.

Factorization of $x^6-729$ is $(x+3)(x-3)\left(x^k+3x+9\right)\left(x^k-3x+9\right)$. Then find the value of $k$.

$(a+b{)}^3-(a-b{)}^3=2b\left(k{a}^2+b^2\right)$. Find $k$.

If $8a^3-b^3-4ax+2bx=\left(2a-kb\right)\left(4a^2+2ab+b^2-2x\right)$, then find $k$.

If after Factorise $a^3+3a^{2}b+3a{b}^2+b^3-8$ is equal to $(a+b-k)\left[(a+b{)}^2+2(a+b)+4\right)$, then find the value of $k$.

The factorization of $2a^3+16b^3-5a-10b$ is $(a+2b)\left[2a^2-4ab+8b^2-k\right]$ then find the value of k.

Factorize $a^6+b^6$. If the answer is $\left(m{a}^2+n{b}^2\right)\left[p{a}^4+q{a}^2{b}^2+r{b}^4\right]$, find the value of $m+n+p+q+r$.