I have 4 hydrangeas that are full of leaves and big but won't bloom. I never cut them back. The only time I cut anything was the first time. One did bloom and it was so gorgeous that I cut the flowers. That was 4 years ago and I haven't had a bloom since. All get full sun except for one that gets a little shade from a cherry tree.
You likely need to prune and your soil may also be lacking phosphorus, which is responsible for flowering. When pruning, make sure not to prune any new stems that grew this past year as these are for blooming next year. If you are not sure which these are, it may be best to wait until spring to prune stems. You can either use a phosphorus rich fertilizer or add some bone meal to the soil. These articles will help you: