I am trying to work on a character sheet that some of the math is done automatically.

I am thinking of using a spreadsheet

Skills work like this though

Level 1 = 1 point

Level 2 = 3 points

Level 3 = 6 points

Level 4 = 10 points

etc

Is there any mathematical way to derive points from level on a spreadsheet?

It depends whether the points allocation based on level follows an algorithm with the level value as an input, or is simply a table with arbitrary point values by level to which you need to reference.

It's not clear to me whether the above is the specific nature of the way points are meant to work, or is simply an example of what a table might look like but the actual points per level may be something arbitrary?