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.