A Boggle might be better-known to interested individuals as either Bogles or Boxels. All of these have been bred from Beagles and Boxers for the purpose of creating a dog that has inherited characteristics of both breeds.
However, you should know that Boggles haven’t undergone generation after generation of breeding for a consistent set of characteristics that purebred dogs have, meaning that they can have a very unpredictable set of characteristics from both sides of their heritage.
Beagles were once intended for beagling, hunting hares and rabbits but not foxes. The name is quite old, but it isn’t certain that the name has always referred to the ancestors of the modern dogs as it seems to have been used as a generic term for smaller hounds. Regardless, these modern dogs are very amicable creatures on the whole. Amusingly, they make good watchdogs because they are prone to barking when they see something unfamiliar, but lousy guard dogs because even strangers can win them over with relative ease.
Meanwhile, Boxers are a kind of German mastiff descended from the German Bullenbeisser and the British Bulldog. Initially, they were formidable hunting dogs, so much so that they were tasked with taking on bears and boars. However, Boxers have since switched over to other roles. In particular, it is interesting to note that Boxers make natural guardians of their families, being patient but protective by nature.
Boggles can be every single one of these things. However, each one is very much their own creature, meaning that interested individuals shouldn’t make too many assumptions about what a particular dog is like based on either Beagles or Boxers.