I built a 4-bit Adder Circuit using the 4008 Adder chip (http://www.doctronics.co.uk/4008.htm). The circuit works fine but there is one problem. I thought it would be able to add any 4 bit numbers or smaller, but my circuit can only add 4 bit numbers! It cant seem to add two 3-bit numbers, or 2-bit numbers etc. Why is this?
Because it's a 4 bit adder, not a 3 or 2 bit adder?
Just expand your 3 bit numbers out to 4 bit with a 0 as the MSB.
Hmmm but for example if i want to input a "4", in binary it would be "100", but i have to input 4 bits right? that means adding a "0" to the "100"? that makes it "1000" and that is "8" in decimal 
No, you add the 0 to the MSB, not the LSB:
8421
0100
Other end. You would add the 0 as the MSB (Most Significant Bit), so 4 (100) would become 4 (0100).