Welcome Kymco Owners!
Yes, 125ccm you ride in most of EU with your "car B" license, (after some additional training and a juicy payment) for more, i.g. a 150ccm, a motorcycle license is required, with which you can ride any bigger/ stronger motorcycle.
@Neil, didn't know that about UK. Here for vehicles under 50 ccm you just need a training class (for a good fee of course), that's why a lot of people with their license taken for DWI drive/ ride this minicars and drinking happily further on.