I would do like MadDog suggests and check any FAQ pages that your host runs as you may find that they have a special folder for databases that has read and write permisisons, many do.
If they do you need to move the database to this folder, then follow the instructions in the forum documentation that comes with the forum on which files have to be edited to point the forum to the location of where the database has been moved to.
If your host doesn't have a special folder for database contact them to change the permissions. Also it is worth following the documentation anyway on moving the database otherwise your forum will be open to hackers who will be able to download the database.