Partial formatting of cell text is a recent addition to Google Sheets, and it is still pretty fragile. The following works:
- Select a cell
- Press Ctrl-C (or Command-C)
- Select another cell
- Press Ctrl-V (or Command-V)
Other methods, described below, are not as successful.
If one double-clicks a cell, selects all of its content, and copy-pastes that, the partial formatting may or may not be preserved (depending on the previous state of clipboard).
If one double-clicks a cell, selects some of its content, and copy-pastes that, the partial formatting is not preserved.