Playing With Numbers

Prove that if $$a$$ is an integer, then $${a^3} - a$$ is divisible by $$6$$.Also deduce that $$5{a^3} + 13a - 30$$ is divisible by 6.
A, CD, GHI, .... UVWXY
If $$k$$ is any even positive integer, then $$(k^{2} + 2k)$$ is
$$50B$$ is a number divisible by $$5$$, what might be the value of $$B$$? 
Check whether $$6582$$ is divisible by $$4$$?