This is a working hand cranked Babbage Difference Engine made using LEGO parts. It can evaluate any polynomial of the form aX^2 + bX + c for X:0 through N with answers to 3 digits.
For this video the machine is set to calculate the squares of the integers. The video shows the computation from X=2 through 8. It will output 4, 9, 16, 25, 36, 49, and 64.
See other mechanical devices I've built at: http://acarol.woz.org