if $a^3 + 2b^3\equiv 0 \pmod {27} $, then $a\equiv b \equiv 0 \pmod 3$ if  $a^3 + 2b^3\equiv 0 \pmod {27}$, then $a\equiv b \equiv 0 \pmod 3$
could you please show this. I am just able show $a\equiv b \pmod 3$

Hint: First show that any cube is congruent to $-1$, $0$, or $1$ modulo $9$.
