ed is correct, but only in a way. Yes, if the cows are homo black all of the calves will be black, but not all of the calves will look black because there is there is another gene at play here. Charolais carry a "masking" gene. When the masking gene is homo, it produces white. When the masking gene is hetro, it produces smoke. Since Gold Mine is obviously hetro for the masking gene (one copy of it, not 2), around 1/2 the calves should be smokes & 1/2 should be black.
The other thing that needs to be considered is that Gold Mine actually is a red animal (2 sets of the red gene), but he looks "frosted" because of the way the masking gene works (think Mello Yellow & Orange Crush). So, even though 1/2 the calves will be black & 1/2 will be smokes, all of them will carry the red gene.
Simmental have what is called a dilluter gene & it is very similar to the masking gene, but the diluter gene throws more yellows (red) & mouse colors (black).
Someone correct me if I am wrong, but I am pretty sure that I am correct.
Hope that helps.