Binomial Coefficient Equivalency

[TranscendArcu]

Find an expression that is identical to \sum_{k=0}^n \binom{3n}{3k}

According to Wolfram, the correct solution to this is: \frac{1}{3} \left(2(-1)^n + 8^n\right)

But I'm not sure which identities of the binomial coefficient I'm supposed to use to prove this. Can anyone give me some direction?

Thanks!

 

[TranscendArcu]

Does nobody have any ideas? I was wondering if it were possible to confirm Wolfram's answer via induction, but expanding the resulting binomial coefficients fron the n-1 to the n case is proving to be fairly difficult. Any help is appreciated.