I came across this question: Sum the series $${6n \choose 0} + {6n \choose 3} + {6n \choose 6} + \cdots + {6n \choose 3n}$$
I tried putting different values of $n$ and tried to find a pattern in the sum, but was unable to get it. e.g.
When $n = 1 $ , $Sum = {6 \choose 0} + {6 \choose 3} = 21$
When $n = 2 $ , $Sum = {12 \choose 0} + {12 \choose 3} + {12 \choose 6} = 1145$
When $n = 3 $ , $Sum = ({18 \choose 0} + {18 \choose 3} + {18 \choose 6}) + {18 \choose 9} = 68001$
Please provide any hint to solve the question.