I am having trouble with this proof.
If $a,b$ are integers, then $(a+b)^3 \equiv a^3 + b^3 \pmod{3}$
What I am confused about is using the definition of modulo. So can $b^3 \pmod{3}$ be written as $3\, |\, [b^3 - (a+b)^3]?$ How does the $a^3$ term come into play with writing the modulo definition.
Also I apologize for the messiness of the math equations, I am new to math exchange and haven't gotten the TeX concepts down yet.
Hint: Just expand $$(a+b)^3 = a^3+?+?+b^3$$