A sum of money is an amount of money.

A sum is a simple calculation in arithmetic.

In mathematics, the sum of two numbers is the number that is obtained when they are added together.

The sum of something is all of it.

You use in sum to introduce a statement that briefly describes a situation.

If you say that something is more than the sum of its parts or greater than the sum of its parts, you mean that it is better than you would expect from the individual parts, because the way they combine adds a different quality.