Number Puzzle

[Davemano]

Missing number 1 8 9 64 25 216 49 ?

[katwoman]

have seen it as 512 dont know how its worked out

[Davemano]

I'm stuck - can't see why 512, but thanks anyhow Katwoman

[teacher1]

The next three numbers are 512, 81 and 1000.
The series goes as 1 squared, 2 cubed, 3 squared, 4 cubed and so on.

[Fibonacci]

1 = 1 x 1
8 = 2 x 2 x2
9 = 3 x3
64 = 4 x 4 x 4
25 = 5 x 5
216 = 6 x 6 x 6
49 = 7 x 7
so continuing the pattern of square and cube numbers
512 = 8 x 8 x 8

[Davemano]

Simple when you see the reasoning and thanks to all for your time