ANSWER
The correct choices are:
[tex] {8a}^{15} - 27[/tex]
and
[tex]216 {a}^{6} - 27 {y}^{3} [/tex]
EXPLANATION
A difference of perfect cube is of the form:
[tex] {(m)}^{3} - {(n)}^{3} [/tex]
We can rewrite
[tex]216 {a}^{6} - 27 {y}^{3} [/tex]
Try rewriting the terms as powers to an exponent of 3.
[tex]216 {a}^{6} - 27 {y}^{3} = {6}^{3}( {a}^{2})^{3} - {3}^{3} {y}^{3} [/tex]
This implies that:
[tex]216 {a}^{6} - 27 {y}^{3} = ( 6 {a}^{2})^{3} - {(3y)}^{3} [/tex]
Hence this is a difference of perfect cube.
Also, we can rewrite
[tex] {8a}^{15} - 27[/tex]
as
[tex]{8a}^{15} - 27 = {2}^{3} ( {a}^{5})^{3} - {3}^{3} [/tex]
[tex]{8a}^{15} - 27= {(2{a}^{5})}^{3} - {3}^{3} [/tex]
