There have been stories through the years of mare mules giving birth, but to my knowledge, none have been substantiated. Male mules should always be castrated to prevent the dangerous behavioral problems inherent in studs. This castration is called gelding, and a castrated mule is known as a gelded mule, or simply a horse mule. In Europe you might hear him called a John mule. The female mule is known as a mare mule or a molly mule.
Most horse people prefer geldings, while most mule people prefer mare mules.
The mares tend to be easier to train. Mules will often grow to a size larger than either parent, and they live longer than the horse. They tend to have more endurance and strength than a horse of the same size, and they tend to be easier keepers. As a general rule, a mule will stay fat on pasture where a horse might not do so well. No need for fancy supplements either.