Clap your hands say yeah right

Here is a variant of this proof:

(… and sorry for the fact that it is jotted on a piece of paper & that the image quality is crap. I am at the nursery this week (trying to get my son compatible with the routines there) and I only have an iPhone at my disposal)

UPDATE: I was a bit sloppy when writing down the proof. Not only is it written in Swedish … it also contains two small typos. The denominators which are written as 2:s should of course have been squared too. They should be 4:s …

UPDATE 2: I was asked for some clarifications. Here we go:

Let C_n be the sum of the cube-series at n.
Let S_n be the sum of the squared series at n.

If C_n and S_n grows with the same delta for each n, then C_n = S_n for all n.

The delta for C_n between n and n-1 is:
C_n – C_n-1 = n³ (trivial).
The delta for S_n between n and n-1 is:
S_n – S_n-1 = … = … = n³ (as shown on the paper on the photo).

Hence C_n = S_n for all n.