Boil corn syrup in microwave. Add white sugar and stir well. Return to microwave and reheat until boiling.
Add peanut butter to sugar/syrup mixture and stir well.
Quickly pour peanut butter/syrup/sugar mixture into mixing bowl with cereal. Stir well (but fast!) and then transfer to a pan or baking sheet. *NOTE: This step, and the one following, must be done as quickly as possible because as the corn syrup cools the cereal mixture becomes harder to spread.*.
Form mixture into one big rectangle about 3/4 inch thick. Cool in fridge for 1 hour.
After its cooled the cereal rectangle may be cut into bars or squares. An alternative is to break the rectangle up by hand into pieces.
Please note that cheerios should not make up more than 1/3rd of the mix as they absorb the corn syrup. If you need to use more cheerios (or other absorbent cereal) then add a bit more corn syrup.