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?

${(x+3)^3 = x^3 + 3^3}$
Expand
${x^3 + 9x^2 + 27x + 27 = x^3 + 27}$
Cancel
${9x^2 + 27x = 0}$
Factor
${x(9x + 27) = 0}$
${9x(x + 3) = 0}$
Therefore ${x = 0, x = -3}$
