What tutor @ikleyn says is true -- trying to answer ANY question like this is ultimately a waste of time, because there is no way to know if any answer you come up with is the "right" answer.
Given any sequence of numbers, if there is no information about what kind of sequence it is, then the next numbers can be ANY numbers.
If you want to take a little time to see if you see a pattern in the given numbers, that is fine... but realize that any answer you come up with might be "wrong".
In this example, there is a clear pattern which makes it VERY LIKELY what the next four digits are:
1 8 27 64 125 216 343 512 729 1000 1331 1728
1^3 2^3 3^3 4^3 5^3 6^3 7^3 8^3 9^3 10^3 11^3 12^3
The PROBABLE next four digits are 13^3 = 2197