Answer
False.
Work Step by Step
In the formula for the sum of cubes,
$A^{3}+B^{3}=(A+B)(A^{2}-AB+B^{2})$,
replacing A with x, and B with a,
$x^{3}+a^{3}=(x+a)(x^{2}-ax+a^{2})$,
so the statement is false.
ALTERNATIVELY,
we can multiply the polynomials by distributing:
$(x+a)(x^{2}+ax+a^{2})=x(x^{2}+ax+a^{2})+a(x^{2}+ax+a^{2})$
$=x^{3}+ax^{2}+a^{2}x+ax^{2}+a^{2}x+a^{3}$
$=x^{3}+a^{3}+(2ax^{2}+2a^{2}x )$
$\neq x^{3}+a^{3}$
so the statement is false.
