If a+2b=5; then show that: a^3+8b^3+30ab=125

If you use the method of factoring third power polynomials with the first and last terms as perfect cubes (which you have here if you simply adjust the order and move the 8b^3 to the last spot), you will see that the second equation is factorable to the following:

(a + 2b)(a + 2b)(a + 2b)

And if each of those were equal to 5, then when you multiplied them all together, you would get 125.