It depends on which way you breed it. But then again I don't know if Cuckoo and Barring are the same.
If they are, you can sexlink them by breeding a "black copper" rooster to a cuckoo hen. Roosters will have barring.
You know there is a great section on the French Marans web site on cross breeding the different varieties. They do not recommend breeding the varieties which are not genetically similar. So apparently the Black Copper, Blue Copper, Blue and Birchen are genetically similar. But the cuckoo is different. Here is the link if you are interested. It is translated from French so the terminology is a little odd but it's readable. The French have different names for the varieties- Black Copper is Brown Red, Blue Copper is Golden Blue and Blue is Silver Blue: