Find the next number in the following series:
220, 221, 229, 256, __

Let us look at the differences between successive numbers in the series:
* $221-220=1=1^3$
* $229-221=8=2^3$
* $256-229=27=3^3$

The differences are perfect cubes of consecutive natural numbers: $1^3,2^3,3^3,\dots$
Following this logic, the next difference must be $4^3=64$.

Therefore, the next number is:

$$256+64=320$$