Explanation:

series 1,1,4,8,(),27,16,64
 Two series 
 one series  is square 
 2nd series is cube

1^2=1 1 square
 square of 1st number
1^3=1    1 cube
2^2=4    2 square
2^3=8    2 cube
3^2=9    3 square
3^3=27   3 cube
4^2=16   4 square
4^3=64    4 cube