I have a number sequence problem.

1,8, 27,64, 125

The answer is 216 in the back of the book. I don't see the pattern. WOuld you point it out for me?

Try successive cubes.

2^{3}=8, \;\ 3^{3}=27, \;\ 4^{3}=64,..............

These are cubes of successive numbers - 1*1*1=1 and 2*2*2 = 8 and so on, after 5, the sequence is 6*6*6 = 216.