Summations

The question:
Let S_1 be the sum of all square numbers between 1 and 10,000 (inclusive)
Let S_2 be the sum of all cube numbers between 1 and 10,000 (inclusive)
Let X be the sum of all square and cube numbers between 1 and 10,000 (inclusive)
Determine if X = S_1 + S_2
My proposed answer:
No, as X does not include all the double counted numbers i.e. powers of 6 - The question asks to prove it algebraically - Note I'd never encountered summation formulae for things like this but I looked at the formula booklet for my exam board and there are provided formulae - I suppose I'll just use the formula and find both results - Is this what anybody else would do? (As you obviously can't use arithmetic series as the requirements are violated)