Mildew grows on the dirt and body oils left on the fabric, not in the fabric itself. Brush the cushion and work outdoors. On woven cushion fabric, mix 1 cup of bleach and ¼ cup of mild soap per gallon of cold water, let it soak in for up to 15 minutes, blot, and rinse very thoroughly. Then stand the cushion on edge until it is completely dry, underside included: foam holds water long after the cover feels dry. Removable woven covers can go through a cold, gentle machine wash, zipped closed, then air dried. Never put a cover in the dryer.