The series can be explained as follows

Any intermediate term is obtained by squaring the sum of previous term and 3.

0, (0+3)^(2), (9+3)^(2), (144+3)^(2), (21609+3)^(2)

Therefore the next term in the sequence is

(21609 + 3)^(2) = (21612)^(2) = **467,078,544.**