Answer
$27x^3+27x^2y+9xy^2+y^3$
Work Step by Step
According to the Binomial Theorem or Binomial expansion, the expansion for $(x+y)$ in the any number of power can be calculated as:
$(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$
Let's see how this formula works:
$(3x+y)^3=\displaystyle \binom{3}{0}(3x)^3y^0+\displaystyle \binom{3}{1}(3x^{2})y^1
+\displaystyle \binom{3}{2}(3x)^1y^2+\displaystyle \binom{3}{3}(3x)^0y^3$
or, $=27x^3+3(9x^2)y+9(x)(y^2)+y^3$
or, $=27x^3+27x^2y+9xy^2+y^3$
