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Your answer equals to =x³+3x²y+3xy³+y³ . 
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There is a shorter way of cubing binomials.
1.) Cube the first term.
2.) Square the first term, then multiply it to the second term, then multiply by 3.
3.) Square the second term, then multiply it to the first term, then multiply by 3.
4.) Cube the last term.
5.) Combine them together.
( x + y)³
2.) x², x²y,         3x²y 
3.) y², xy²,         3xy²
5.) x³ + 3x²y + 3xy² + y³

Final Answer:
                   x³ + 3x²y + 3xy² + y³

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