Prove that \(\displaystyle \sum_{m=0}^n \sum_{i=0}^m \binom{n}{m} \binom{m}{i}^3=\sum_{m=0}^n \binom{2m}{m} \binom{n}{m}^2\).

The best solution was submitted by Chiheon Kim(김치헌), 수리과학과 2006학번. Congratulations!

Here is his Solution of Problem 2010-6.