Find the next number in the following series:
$$220,221,229,256,\underline{}$$

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

The logic of the series is that the cubes of consecutive natural numbers ($1^3,2^3,3^3,\dots$) are being added to the terms.
Following this pattern, the next difference must be $4^3=64$.

Therefore, the next number is:

$$256+64=320$$