I am very new to Houdini but I am trying to make a whale breaching. My problem is when I render I get theses weird black spots on my model. I think they are shadows but I am unsure. I have attached an image of the render below.

To me, this doesn't really look like a shadow, more like artifacts from the model. In Mantra, you can enable some different AOVS in the Extra Image Planes Tab to see where this is coming from if this is connected to shadows/rendering. Otherwise, I would take a deeper look at the model and textures that came with it. I've experienced cases where textures/geo would break after adding subdivision because the model wasn't set up properly.

It almost looks like two different versions of the model are superimposed. Double-check render candidates to make sure collision and other not-to-be-rendered objects are hidden.