Summing the terms of a series I have a really confusing question from an investigation. It states-
Find the value of:
$$\sqrt{1^3+2^3+3^3+\ldots+100^3}$$
How would I go about answering this??

There is a nice visual proof (of concept) of the Nicomachus's theorem: the sum of first cubes is a squared triangular number:

So the square root of the total volume of the cubes above is the side of the square below, hence the sum of the first integers. 
In this  example, you have $225$ "unit cubes", whose root is $15$, i. e. the length of the side of the square below.
It takes some more time to draw $100$ increasing cubes, but the proof works along the same lines.
