Is there any value for $x$ that would make the statement $(x+3)^3 = x^3+3^3$ true? 
Is there any value for $x$ that would make the statement $(x+3)^3 = x^3+3^3$ true?

I understand that when factored out, you have $(x+3)^3 = x^3+9x^2+27x+27$ as opposed to the other side which is $x^3+27$, so even if you plug in $0$ the left side will always be greater. Is this the right thinking process for determining the answer? Or am I missing something?

$(x+3)^3 = x^3+3^3$
$\Leftrightarrow x^3+9x^2+27x+27 = x^3+27$
$\Leftrightarrow 9x^2+27x = 0$
$\Leftrightarrow x^2+3x = 0$
$\Leftrightarrow x(x+3)=0$
$\Leftrightarrow x=0$ or $x=-3$
