cement cracked around mailbox
To determine why the footing broke some more information on the footing such as hole depth, diameter, climate as well as what your cement mix was would be helpful.

My best guess as to why the cement cracked would be that it was not mixed correctly, or simply not enough cement to hold the mail box.

I would not recommend trying to shore it up, in my experience that is always more trouble than it is worth. Your best bet is likely to dig it out and put in new concrete. You said you are looking for a simply solution so take a look at Quikrete or something similar depending on where you are and what you can get. The premixed Quikrete stuff is dead easy just add water and fill the hole.

I like to overbuild so I would make sure the hole is 3+ feet deep, minimum 8 inches diameter and I would set a 4x4 to hold the mail box.