are you sure it is algae? After three weeks, there should be a nice build up of gunk on your filter just from the filtering process. Excessive waste, like overfeeding or a croweded tank will make this stuff builld up faster. It is slimy and brownish color. If you have a lot of algae floating in the water (like, your water is discolored with algae) leaving the lights off for a week and doing some small water changes every couple of of days during that time can help clear it up. If it is really bad, it might take longer.
I had a really bad case of green algae in one of my tanks and I WISH my filter would have cleaned it up, but the filters really don't do much to algae.
This gunky build up isn't all bad. A lot of good bacteria lives in that slimy mess. If your filter is still working fine, i.e. the water isn't flowing over or around the filter media because it is so clogged up, then you don't have anything to worry about. Try going four weeks one time and see if the water starts going around the filter media. If not, then if changing it every three weeks is a hassle, then wait four weeks. I really wouldn't leave it in any longer than that anyway.