I'm not crazy about this question. Here's why:
Take: $a^2+2ab+b^2=9$
Factor to get: $(a+b)(a+b)=9$
In other words: $(a+b)^2=9$

So, EITHER $(a+b)=3$ OR $(a+b)=-3$

If $(a+b)=3$, then $(2a+2b)^3=[2(a+b)]^3=[2(3)]^3=6^3=216$.
Answer: E

If $(a+b)=-3$, then $(2a+2b)^3=[2(a+b)]^3=[2(-3)]^3=(-6)^3=-216$
Since $-216$ is not among the answer choices, the question should read something like: "If $a^2+2ab+b^2=9$, then $(2a+2b)^3$ COULD equal"

Cheers,
Brent