Exponent Extravagant

Let $S(n)=1^2+1^3+2^2+2^3+...+(n-1)^2+(n-1)^3+n^2+n^3$ , then:

$S(n) = \sum_{i=1}^{n}{i^2}+ \sum_{i=1}^{n}{i^3}$

$\quad = \frac{1}{6}n(n+1)(2n+1)+\frac{1}{4}n^2(n+1)^2$

Therefore, $S(200)= \frac{1}{6}(200)(201)(401)+\frac{1}{4}(200^2)(201)^2$

$\quad \quad \quad \quad \quad \quad \quad =2686700 + 404010000 = \boxed{406696700}$

1^2 +2^2+3^2 + ...+ 200^2 =1/6(200)(201+1)(2*201+1). And 1^3 +2^3+3^3+.....+ 200^3 = ((200)(201)/2)^2. And the total sum is 406696700