Is it possible to speed up a sum() in MySQL?

No, you can't speed up the function itself. The problem here is really that you're selecting 7.3 million records. MySQL has to scan the entire table, and 7.3 million is a pretty big number. I'm impressed that it finishes that fast, actually.

A strategy you could employ would be to break your data into smaller subsets (perhaps by date? Month?) and maintain a total sum for old data that's not going to change. You could periodically update the sum, and the overall value could be calculated by adding the sum, and any new data that's been added since then, which will be a much smaller number of rows.