DD is five and can do similar things (she's in Reception). School sent a maths worksheet home suggesting she work on 'the story of 2' which is, thrillingly, the fact that 0+2, 1+1 and 2+0 all add up to 2. Have ignored it. She can add eg 12+10 or 21+7 in her head without missing a beat. She worked out herself that if you know 5+5 and want to know 6+6, the answer must be two more than 5+5. The class goal this term was to order and write numbers up to ten, count objects up to ten and think about one more and one less which is pretty dull for her, though she doesn't really mind. She's a pretty well-behaved and sensible child and always pays attention even when things are easy for her which I kind of suspect might take her further than her early facility for arithmetic!
We are just pootling on with more interesting things at home, like odd and even numbers - we did an experiment with raisins to see how some are odd and some even and if there's a rule, and she's now busily pointing odd and even numbers out all over the shop. We are also dividing by three and four and five with raisins as props - then eating one or more and seeing what happens. She informed me (unprompted, following a period of unaccustomed silence and visible cog-turning) a couple of years ago that if you had a basket of three things and two more baskets of three things then you'd have nine things and three baskets. Bar charts have also been v interesting for her. And she is very intrigued by Venn diagrams and sets of things and what makes something be part of a set.
We also got a great book called something like Sandbox Science from Amazon, which has ideas for 'experiments' you can do at home - not strictly maths but it has given me a great jumping off place to think of fun stuff. Some of it requires you to get hold of equipment, but even the things we haven't been able to source have given me ideas for other activities. For a child who has a natural facility with numbers some early science activities can be very absorbing and perhaps a kind of sideways stretch.
Hope this gives you some ideas of things you could do with your son that might interest him! I'm under no illusions that DD is going to turn out a genius but in the mean time, we have had a lot of fun with our raisins and bottles of frozen water etc!