No, this is a color variation known as leucism.

First, all Mute Swans are known as Mute Swans or scientifically as Cygnus olor. However, swan keepers may refer to the Mute Swans as "Royal" or "Polish".

The "Royal" Mute Swan has black legs and feet, reddish orange bills and taupe (gray) colored cygnets (baby swans). This is the normal coloration.

Many centuries ago, someone in eastern Europe decided to try and produce an all white swan, commonly known as albino with no color pigment.

They were very unsuccessful and produced a leucistic coloration known as a "Polish" Mute Swan. The swans still have color pigments, but are very light in color. Polish Mute Swans have taupe (gray) colored legs and feet, orange bills and their cygnets are white in color.

So, what you are seeing is the color variations between the cygnets and one or both parents carry the recessive gene that produces the leucistic coloration. This has nothing to do with gender. The Regal Swan