update_all makes an sql query, so any processing you do on the values needs to be in sql. So, you'll need to find the sql function, in whichever DBMS you're using, to add two numbers together. In Postgres, for example, i believe you would do

Sum.update_all(sum: "x + y")

which will generate this sql:

update sums set sum = x + y;

which will calculate the x + y value for each row, and set the sum field to the result.

EDIT - for MariaDB. I've never used this, but a quick google suggests that the sql would be

update sums set sum = sum(x + y);

Try this first, in your sql console, for a single record. If it works, then you can do

Sum.update_all(sum: "sum(x + y)")

in Rails.

EDIT2: there's a lot of things called sum here which is making the example quite confusing. Here's a more generic example.

set col_c to the result of adding col_a and col_b together, in class Foo:

 Foo.update_all(col_c: "sum(col_a + col_b)")

I just noticed that i'd copied the (incorrect) Sum.all.update_all from your question. It should just be Sum.update_all - i've updated my answer.