The Cicada Killer is a species of large wasp. The female stings a cicada to imobilize it. It then carries the cicada to a ground borrow where it then lays its eggs on the cicada. When the eggs hatch, the larva of the wasp utilize the body of the cicada for food.
Cicada Killer or Mason Wasp
Cicada Classical Greek , it was called a Greek tzitzikas both names being the cicada killer wasp and praying mantis.
This insect is called a cicada killer, a giant wasp that ranges from 20-40mm. The cicada killer paralyzes cicadas with it's stinger, sometimes in mid-flight, and drags the cicada down into it's burrow. It then lays it's eggs on the cicada, and it's larvae eat it.
From your description, it sounds like either a Hornet or a Cicada Killer.
I too have a large red bee with a red back that dug a hole in my lawn. I can't find any information about this insect.
The cicada wasp looks exactly like a yellow jacket. The one major feature of the cicada wasp that sets it apart from a yellow jacket is its size. The cicada wasp is as much as 4 times as big as a yellow jacket.
The black wasp is an aggressive bee. Another name for the black wasp is the cicada killer wasp. It is larger than other wasp, growing up to 2 inches long.
It sounds like you are describing a cicada killer wasp. These large wasps are solitary and are known for their habit of digging holes in the ground to create nests for their young. Though they can look intimidating because of their size, cicada killer wasps are generally not aggressive towards humans.
A bee or wasp
The Cicada Wasp has a black body with blue wings. This wasp also features red and yellow stripes near its stinger.
I was just browsing for this question myself and found that they do not unless they are provoked. http://www.masterbeekeeper.org/stinging/cicadakiller.htm