Today I discovered that Autodesk offers a lot of its 3D modeling products for free (for educational purposes).
Here are the one I was most interested in, but there are more. These are the prices you would normally pay, just for reference.
AutoCAD: $1,470.00 /year
3ds Max: $1,470.00 / year
MAYA: $1,470.00 / year
Inventor: $1,890.00 / year
saving: $6,300 / year
They do not really check for the email (but send a confirmation link), so you can use a spam mailing service to download the software and get the license keys. If I got it right, they expire after 3 years? Nonetheless a great deal if you ever wanted to have professional software for 3d modeling.
A free (and open-source!) alternative is Blender and, once you get how it works, it is a really great 3D modeling and video editor.