Select the related word/letters/number from the given alternatives.
9:27::64:?

Let's establish the relationship in the first pair:
9=3
2

27=3
3


Applying the same logic to the next set:
64=4
3
(or 8
2
)

If we use the square-cube logic of the same base:
Since 64=8
2
, the next number should be 8
3
=512.