Olá,
jomatlove.
Usaremos que
[tex3](a-b)^3 = a^3 -b^3 -3ab(a-b)[/tex3]
Note que
[tex3]\begin{aligned}(2021 - 2019)^3 &= 2021^3 - 2019^3 - 3\cdot 2021 \cdot 2019 ( 2021 - 2019) \\ & = 2021^3 - 2019^3 - 3\cdot 2021 \cdot 2019 \cdot 2, \end{aligned}[/tex3]
ou seja,
[tex3]2021^3 - 2019^3 = 8 + 6\cdot 2021 \cdot 2019[/tex3]
Segue, daí, que
[tex3]\begin{aligned}\sqrt{\frac{2021^3 -2019^3 -2}{6}} & = \sqrt{\frac{8 + 6\cdot 2021 \cdot 2019 -2}{6}} \\ & = \sqrt{\frac{8 + 6 \cdot (2020 +1)(2020-1) -2}{6}} \\ & = \sqrt{\frac{8 + 6(2020^2 -1) -2}{6}} \\ & = \sqrt{\frac{6\cdot2020^2}{6}} = 2020.\end{aligned}[/tex3]