The gene for color is found on the X chromosome. Females have two copies of the X chromosome. Albino color (or lack of it) is recessive to black and red. If the female cat is black, one of her X chromosomes carries black and so does the other.
A male carries one X and one Y chromsome. Again color for coat is found only on the X.
In the first case, she produced eggs with one X in each. Each carry the black gene. The male produces X and Y sperm. On the X chromosome he has a recessive for lack of color of the coat. Nothing for coat color is on the Y.
The female is BB (black) her eggs are B
The male is bb (albino) his sperm are b.
Combined form Bb (kittens) which is black for coat color and recessive for albino.
Crossing the same male bb with a female that produces a litter with black and white kittens means that she is black but is recessive for albino. She is Bb.
The kittens are bb or Bb. The ratio should be 3:1 but that would be seen with a much larger number of litters.