ANSWER
[tex]- 27 {a}^{3} {b}^{6} + 8 {a}^{9} {b}^{12} [/tex]
EXPLANATION
When we can write an expression in the form
[tex] {(x)}^{3} + {(y)}^{3} [/tex]
then it is a sum of cubes.
To write a given sum as sum of cubes, then the coefficients of the terms should cube be numbers and the exponents of any power should be a multiple of 3.
This tells us that the first option will be the best choice.
[tex] - 27 {a}^{3} {b}^{6} + 8 {a}^{9} {b}^{12} [/tex]
We can rewrite this as:
[tex] { (- 3)}^{3} {a}^{3} {b}^{2 \times 3} + {2}^{3} {a}^{3 \times 3} {b}^{4 \times 3} [/tex]
We apply this property of exponents:
[tex] ({a}^{m} )^{n} = {a}^{mn} [/tex]
This gives us
[tex] {( - 3a {b}^{2}) }^{3} + {(2{a}^{3} {b}^{4} })^{3} [/tex]
Therefore the correct option is A
