Answer
Quotient: $x^2+xa+a^2$
Remainder: $0$
Work Step by Step
$\space$$\space$$\space$$\space$$\space$$\space$$\space$$\space$$\space\space$ $x^2+xa+a^2$
$x-a$$\space)\overline{x^3+0x^2a+0xa^2-a^3}$
$\space\space\space\space\space\space\space\space\space\space\space\space\underline{x^3\space-x^2a}$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space x^2a+0xa^2$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\underline{x^2a-xa^2}$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space xa^2-a^3$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\underline{xa^2-a^3}$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space \space\space\space\space 0$
Check answer:
$(x^2+xa+a^2)\cdot(x-a)+0$
$x^3-x^2a+x^2a-xa^2+xa^2-a^3$
$x^3-a^3\checkmark$
