Cub is brought to Marcus as a very young pup: his eyes are open and he has teeth but he's not very mobile and he's not weaned. This adds up quite neatly to suggest he is about 15 days old when Esca takes him from his den in, say March of the year after Marcus is wounded.
As the key socialisation period for wolf cubs ends around 19 days (much earlier than dogs) he is the right age to become - well, as socialised as a wolf is ever likely to become, anyway. So he has a relatively good opportunity to integrate into a human household.
During the period covered by the book, Cub is a juvenile wolf. Wolves don't start hunting until they are about a year old, and as cubs, tend to behave in a more doglike manner than adult wolves, though they are still very active and need a lot of exercise and can be rough (as Marcipor found out when his toe got bitten, which is book canon).
Although Marcus thinks that Cub is fully grown the spring after he got him, Marcus is wrong : Cub may look adult, but he's got at least another year before he is physically mature, and that's why he still behaves like a puppy (at least, when greeting Marcus, his Mum). It's not surprising that Cub comes rushing home when Marcus takes his collar off: Cub isn't old enough at just over a year old to live on his own and still needs help from (and is closely bonded to) his family.
Wolves bond very strongly with their families and don't handle change well. When Cub does his appeasing puppy wagging thing with Marcus, from Cub's point of view he is greeting his Mum. You would not expect Cub to greet other humans as enthusiastically, and in fact, he doesn't.
Marcus is Cub's special human being. Cub is also prepared to take food from Esca, Cottia, and, when Marcus is about and Cub is feeling relaxed and confident, Sassticca. When Marcus, Esca and Cottia all go away and leave Cub in Calleva, he pines and almost starves himself to death. This is pretty unusual behaviour for a dog (a grieving dog may skip a few meals, but won't generally starve himself), but is apparently very typical of wolves and is one of the many reasons that they make terrible pets. Wolves need and expect to be with their family most of the time.
What sort of wolf would Cub have been? Could he be a wolf-dog?
Cub would be a British gray wolf, and British wolves are three centuries dead - more specifically, Cub is supposed to be a wolf from the Calleva area, and there have been no wolves in central-south England for at least five hundred years. British wolves were probably quite similar to wolves in the rest of Europe, but we can't be sure. Even when canid bones are found, it's often hard to tell if they are wolves or dogs, unless they are unusually well preserved.
British wolves lived on a relatively small island, isolated over a long period from other wolf populations, but with an awful lot of people and dogs. If Cub doesn't behave like a typical European wolf, then maybe that's because British wolves were not typical European wolves. It's an argument that would be hard to disprove.
Genetic tests have shown that modern wolves in Bulgaria have interbred with feral dogs (wolves are the same species as dogs, just a different subspecies). So, Sutcliff's fictional idea of a wolf and dog population that interbreeds fairly regularly is possible. It seems to be more typical for wolves, in most of the places where you get wolves, to eat dogs than mate with them, but presumably that depends on the size and temperament of the dog. During the Roman period, there are several references to Britain as a source of particularly impressive hunting dogs (though whether interbreeding with wolves would have produced a better working hunting dog is open to question, as wolves are typically shy and not very obedient).
One thing that supports the idea that Cub is a wolf-dog is that he is described as 'brindle'. Brindle is a quite specific colour pattern (like a tabby cat) and so far as I can find out, it does not normally appear in wolves, only in dogs.
What might happen to Cub?
Adult pet wolves tend to be quite challenging and risky for people to be around at close quarters. This causes people to start talking about 'alphas' and 'dominance'. David Mech, who did the original study that came up with that idea, has since decided that isn't how wolves work in the wild. However, the reasons may not seem that important if you happen to own a pet wolf and have to deal with difficult adult behaviour - because there is no way that a pet wolf can behave the way that his genetics says he should.
Once he is fully adult, the natural thing for a wolf to do is to find a territory and a mate and start having cubs to form a pack of their own. For modern pet wolves, this is a major problem, because modern pet wolves have no hunting skills, little idea how to interact with other wolves and don't have a spare 16 square miles to live in. They haven't had the practice to do well in the wild, and they aren't genetically predisposed to remain eternal puppies, like dogs.
Unlike modern pet wolves, Cub has probably spent a fair bit of his time hunting, he's canonically well socialised with other canids, and he lives in a place where there is plentiful wolf habitat, and territories which regularly become available (due to regular wolf hunts). So: possibilities:
1) he slips away to find a mate. This is likely to be bad news for the sheep and small children of the Calleva area once he gets hungry, because Cub isn't scared of people and is used to thinking of them as a food source.
2) Esca realises that Cub hasn't worked out as a dog and kills him before he eats someone. Oh! the angst!
3) Cub actually does eat a baby or someone's beloved dog, and Marcus has to kill him (because, let's face it, Marcus would not spot the problem before it happened). Even more angst!
4) if Cub is a wolf-dog who has ended up with mostly dog genes (this can happen with second generation crosses, even if both parents look and behave like wolves and the pup looks like a wolf) - then he might just manage to actually become a dog, if a rather shy one with separation anxiety issues that needs a lot of exercise.
This still isn't necessarily a happy-ever-after though. Because Cub has been removed from his mother before he should have been, he may still have health issues - for example, he might go blind early because he's not had the right sort of milk.
International Wolf Centre : http://www.wolf.org
Wolf / wolfdog sanctuary: http://www.missionwolf.com/
Article from Wild Sentry on wolf domestication: http://cf.nwf.org/wildlife/pdfs/canyouturnawolfintoadog.pdf
Wolf Park : http://www.wolfpark.org/
Comparative Social Cognition: From wolf and dog to humans: http://psyc.queensu.ca/ccbr/Vol2/Kubinyi.html
Wolf-to-dog transition had little to do with humans, ancient skull suggests (Evidence for multiple evolutionary wolf domestication events worldwide over a long period) http://news.nationalpost.com/2011/12/18/wolf-to-dog-transition-had-little-to-do-with-humans-ancient-skull-suggests/
Book :Roger Abrantes: the evolution of canine social behaviour
Book: Raymond & Lorna Coppinger : Dogs : a startling new understanding of canine origin, behaviour and evolution.