$\underbrace{a+a+a+ \dots +a}_{\text{n times}}=a^2b$ and $\underbrace{b+b+b+ \dots +b}_{\text{m times}} = ab^2$, where $a, b, n, m$ are natural numbers. What is the value of $\Bigg( \underbrace{m+m+m+ \dots +m}_{\text{n times}} \Bigg) \Bigg( \underbrace{n+ n+ n+ \dots + n}_{\text{m times}} \Bigg)?$

- $2a^{2}b^{2}$
- $a^{4}b^{4}$
- $ab(a+b)$
- $a^{2}+b^{2}$