Look at the pictures above.
The oval cable will have ends crimped on both ends, and the square will measure from .120" to .125" or about 1/8".
The round cable will not have any ends on it and is simply squeezed to make it square. the square end will measure about .100"
The hole in the gear is only square in the bottom half, the first half is round then you get to the square at the bottom. Make sure it is not full of dirt keeping the cable from going all the way in, or make sure your cable is not oversize or has a bur on the end keeping it from going all the way in.
A stripped out square hole in a gear is not a common problem.