please peruse the pdf link directly to Glen Raven Mills, manufacturer of Sunbrella. I'll save you the trouble of clicking the link, and quote directly:
for Stubborn Stains and Mildew
Sunbrella fabrics do not promote mildew growth, however, mildew may grow on dirt and other foreign substances that are not removed from the fabric.
To clean stubborn stains:
Prepare a solution of 1 cup bleach and 1/4 cup of mild soap per gallon of clean water.
Soak affected area in solution for 15 minutes.
Blot stain with a sponge or clean towel. (Note: This step should be avoided when cleaning
the coated side (Back side) of Sunbrella Plus, Supreme, or Clarity.
Rinse thoroughly to remove all soap residue.
Note: Use caution when cleaning the coated (underside) of Sunbrella Plus, Supreme, or Clarity with the recommended bleach solution. The coated side of the fabric should only be sprayed with the recommended bleach solution and rinsed thoroughly.
Remember to protect the area around your Sunbrella fabric if using a bleach solution. Carpet or other fabrics that are not Sunbrella may have an adverse reaction to the bleach."