How do I seal a downspout leak in my shed?

Question

I have a storage shed behind my carport. A downspout from the roof of the carport runs through the shed, as seen in the picture. The downspout drains ok (there was blockage in the past) but it leaks at three of the joints (two shown in the picture). Is there some way to seal the leaks? Or is it a partial blockage problem? Thanks.