You may have an older American Standard Cadet toilet, but ANY toilet can have your symptoms. It is caused by the fill valve NOT supplying enough water into the bowl after a flush to refill it. Your first flush uses most of the water to refill the bowl and there is not enough left after that to make the flush. Once it is full, the second flush performs normally. To prove this, slowly pour water into the bowl until the water level is at its maximum, then flush the toilet.