Not getting the creamy result beating butter and sugar
There may well be more than one issue here.


The type of butter. If you're using what is sometimes sold as "cooking butter" then this has a much lower moisture content than normal butter, and so it is very difficult to get the sugar to dissolve enough to cream.
Sugar choice. Granulated sugar is much more difficult to cream than than caster (superfine) sugar due to the large crystal size.
Recipe proportions. It is more common to use roughly equal weights of butter and sugar when creaming them together; here there is more than twice as much sugar compared to butter, so I am not at all surprised that it is not ending up as a very creamy mixture.


As the aim of the beating process is to dissolve the sugar and to add air, adding one of the eggs and beating well would allow you to achieve both of these.