You may not get any white babies at all!
There are a whole bunch of genes that affect rabbit coat color; it is the interaction of all of them that determines what color a rabbit is. Ruby-eyed White (REW) happens at the C locus (a particular location in the rabbit's genetic code). Blue-eyed White (BEW) happens at the V (for Vienna) locus. These are two entirely different genes; each affects the coat color completely separate from the other. REW is what I call "the lightswitch." It shuts down production of all of the pigment that would normally be in the coat and the eyes. It is also fully recessive, so you know that a REW has two copies of the REW alelle. You can't be sure what a REW carries at the V locus.
BEW shuts down all pigment production in the coat, but leaves the dark pigment at the back of the rabbit's eyes. Since there is some pigment in the eyes, you know a BEW doesn't have 2 REW alleles, but you can't know that it doesn't have one (this is where pedigrees come in; by knowing what colors the rabbit's ancestors were, you have a clue about what the rabbit may have inherited). BEW is also recessive, so you know that a BEW has 2 copies of the BEW allele.
IF the REW has any BEW alleles, you MIGHT get some BEW babies. IF the BEW has a REW allele, you MIGHT get some REW babies. BEW is a strange gene. When a rabbit gets one copy of BEW and one of the normal color alelle, you get a rabbit that may or may not have blue eyes, with a colored coat that has some white markings on it. The white may be as little as a white mark on the nose, or it may look sort of like the markings on a Dutch rabbit. This is called Vienna-marked, and is the result that I would expect from a REW to BEW cross.