Chilla explained it Very well - I like to look at it like 'switches' turned off and on on a horse. Each horse has a set of all the possible switches (2 possible for each color gene) - some are switched on, some off. Each switch changes the appearance of a horse, sometimes if they have both turned on it'll look different from if they have one turned on. Like the cream dilute - on a red base 1 cream gene makes palomino, 2 cream makes cremello. Get where I'm going with this?
So you're mare who can only make black foals - clearly has BOTH Black switches turned on - if one was off there would be a 50/50 chance of her foal getting her black gene (of course what daddy carries can also influence the %)
What's nice about True black horses is you know they aren't hiding anything - there is no dilute gene that isn't visible on a black horse (except sometimes black with 1 cream can be tough to distinguish)
One a red base horse dilutes like agouti(bay) and silver may not be apparent without DNA tests and may show up in a foal.
Now the daddy of your mix is probably the one throwing you some curve balls.
'dun' is just a dilute gene, it could appear on any color. So if the dun daddy a bay dun? Black dun (Grulla)? Chestnut dun? Buckskin dun? What base does he have?
For the sake of this post I'm going to "ASSume" he's a bay dun - because that's what most people refer to as just a plain 'dun'.
This would mean he carries at least 1 black gene, at least 1 agouti (bay) dilute gene, and (because you said he's guaranteed to throw dun foals) he must have 2 Dun dilute genes.
So daddy could look something like
Ee (black 1 switch on, 1 switch off)
Aa (bay 1 switch on, 1 switch off)
DD (dun both switches on)
He could have both switches on for black or bay - but we'll pretend like he doesn't because we don't know for sure.
So daddy has a 50/50 chance of carrying on his E (black gene) but lucky mommy has 2 so foal is definitely going to definitely get the E gene from mom - so baby is 50/50 Ee or EE (one on, one off or both on 50/50)
The agouti (bay gene) only effects black based horses - the foal is definitely is black based so he has 50/50 to get 1 agouti from daddy, but no chance of getting any from mom. So he's 50/50 whether he'll be Aa or aa (1 switch on, 1 switch off or both off 50/50). Luckily it only takes 1 A to effect a black based horse. So foal is 50/50 whether or not he gets the bay gene.
While Daddy is sure to pass on one of his Dun genes, mommy has none - again luckily it only takes one to get dilute the color.
So baby would be either Grulla or Bay Dun :)
Sorry if that went crazy - I LOVE genetics!