Answer
$x^3+12x^2+48x+64$
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:
$(x+4)^3=\displaystyle \binom{3}{0}x^34^0+\displaystyle \binom{3}{1}x^{2}4^1+\displaystyle \binom{3}{2}x^14^2+\displaystyle \binom{3}{3}x^04^3$
or, $=x^3+3(x^2)4+48x+64^0$
or, $=x^3+12x^2+48x+64$
