Move the sofa cushion outdoors immediately. Mildew loves to spread, so you must isolate the affected cushion from the rest of the sofa. If possible, place the cushion in the sun until it dries. If sun-drying is not an option, dry the cushion with a portable heater or hair dryer.
Examine the rest of the sofa for signs of mildew. Since mildew spreads easily, you must ensure that no other parts of the sofa have been affected. If you do find mildew growth on other cushions or on the sofa itself, move the affected parts outside to dry, and clean them the same way that you clean the original cushion.
Vacuum the cushion (along with any other affected areas) with a vacuum hose extension. This will draw the spores out of the cushion and help to prevent regrowth of the dried mildew. Wash out the filter in your vacuum cleaner outdoors before using it again.
Pour 1/2 cup of borax, sometimes sold as boric acid, over 2 cups of hot water. You must use hot water to activate the crystals. Boric acid is a natural pesticide sold in home and garden stores that is especially useful for killing mold and mildew on upholstery.
Scrub the borax solution over the cushion with a soft sponge. Wait at least an hour to allow the borax to do its work, and then scrub the cushion again with a damp sponge to rinse the borax away.
Dry the cushion completely before bringing it back into your home. Use sunlight for best results, or use one of the aforementioned heating methods. If mildew returns, dispose of the cushion. Recurrence may indicate that the spores exist too deeply within the material to be properly removed.