For the white cockerel, do you know what color his parents were?
The white should be either Dominant White or recessive white, which behave quite differently in breeding-- and I cannot find anything that says which one White Australorps typically have

If he had two white parents we still won't know, but if both of his parents were not-white, then he would have to be recessive white.
The expected breeding results each way:
If he has Dominant White, which changes black to white, then he may sire 100% white chicks with all of those hens. Or he may sire 50% white chicks, with the other 50% being black or blue (or splash, if he also has the blue gene hiding under his white color.) The difference (100% vs. 50%) depends on whether he's got one copy of Dominant White, or two copies of it. The "white" chicks might show bits of black, blue, or splash (Paint). This happens when a chicken has only one copy of the Dominant White gene.
If instead he has recessive white, which turns all colors white, then we know he is pure for that gene, because it can only be seen when a chicken has two copies of it. In that case, crossing him to your hens will probably not produce any white chicks at all, although all his chicks would carry the gene for recessive white. If any of your hens carry recessive white, they would produce 50% white chicks and 50% other colors when bred to a recessive white rooster. ("Colored" chicks could be black, blue, maybe splash, maybe something else, depending on what color is hiding under the white of the rooster-- recessive white hides everything, so we can't tell.)
Recessive white chickens would not be expected to have any leakage of black, red, etc. Chickens with Dominant White might show some leakage, but they might not. So if you see any color leakage, he is not recessive white. But a nice clean white does not tell which genes he does have.
And it is also possible for a chicken to have both Dominant White and recessive white, although I think it is more common for them to have just one or the other. If he has both kinds of white genes, you will get a mix of results.