Don't pressure yourself by thinking that you HAVE TO entertain his every waking moment. When he gets older, and more mobile and a toddler, still, don't feel pressured. Kids also need to learn that they "can" entertain themselves. It's all part of development.
Sometimes, just doing "nothing" is great. It gives them the opportunity to have an independent moment. Which is an event for them too and they need un-structured play time too. It's all part of their learning.
Even having a bath is an activity for a baby. He's only 6 months old. Many times, the best way for them to "learn" is to just put them down among their toys or not, and simply let them entertain themselves. Babies learn LOTS this way too. Don't worry. They NEED to explore their world on their own too, without constant intervention. Let him figure things out on his own, let him learn cause and effect on his own, let him touch and feel things. Of course be next to him, but don't feel you have to always stimulate him. Babies are great at doing this on their own too. They need this. They will learn with Anything in their environment, toys or not. Even a simple Kleenex box will entertain them, or a toilet paper roll with toilet paper on it... let him unravel it. Anything is a potential "learning" event and toy.
Give him crayons too. My firstborn was holding a crayon and scribbling at 7 months of age. She had great fine motor skills even at this age already. Experiment. Give him paper and finger-paints and let him try it. Let him make a mess. It's okay. This is how they learn too. I did this with both my kids as babies, and they loved it.
Teach him about "smell." From this age when my kids were babies... I'd show them various spices in the kitchen, and I'd hold the bottle, let them smell it and it was a "sensory" event for them. Then I'd take them in the garden, and let them smell flowers, herbs I grew, leaves, grass, dirt, etc. They really loved this.
"Teach" him about music... put on different kinds of music, and while carrying him, dance away! It will teach him how to "feel" the beat... entertain his senses, and about movement too. It is also a great way to bond, and just have fun.... and exercise too! *oh, and sing to him too! Especially rhyming songs.... they will pick it up and it's great to sing and incorporate music into their lives.
Lie down on your back, put him on top of you, (safely) and while holding him, do sit-ups! There's lots of exercises you can do WITH baby. Use your baby as a "weight" when you do resistance exercises.... or hold him against you, and do squats. All of these things are activities for both of you.
"Teach" him about facial expressions... make funny faces and sounds and then say "happy", "sad", "grumpy" etc. Sure, they can't say it themselves yet, or understand it completely...but, it's about teaching them concepts. And,if you keep it up and teach them it consistently.... as they get older, you will see their level of articulation and "understanding" develop. I began this when my kids were just babies... and before I knew it, they really gained an understanding about "feelings" and what different expressions meant, and it contributed to their development and way of expressing themselves as well. My girl, was very articulate for her age, and things like this all contribute to their "understanding" of their world. Never underestimate a baby's ability... they are sponges, and are storing things in their brain.
Or, get audio tapes or DVD's for babies, which are in other languages. Teaching a baby/child other languages develops their synapses and brain connections differently than in single-language babies/children. You don't have to have your baby literally SIT in front of the t.v., just play it in the background, and they absorb it. My children are bi-lingual....both of them, from before they were even 1 years old, were completely fluent in my Husband's native language of French. They understood both languages more than even I could.
It's amazing what babies CAN and do learn. My daughter now loves to learn languages and about different cultures....she's learned some spanish, japanese, and hawaiian too. I think it gives them a great exposure and "appreciation" of different things and a well rounded base... even as they get much older. And no, letting my children learn different languages did NOT hinder their speaking ability or ability to understand English, their first language. It did not confuse them either.
In the bathtub, put things in it that can get messy... bath paints, sponges, toys, and let him go at it. Then after, you just wash the tub down. Fun and easy.
Both my babies were advanced for their ages as well... sometimes you just have to let THEM lead you... and see where it takes you. They will surprise you. Instead of saying "no no" to things they touch... let them touch it. Supervise of course so they won't get hurt... but let them explore.
Another fun thing to do is: crinkle up all your old newspapers, put it in a huge pile in a corner of your room or in a BIG box...."hide" some toys amongst the crumpled newspapers, and then let him tear into it and explore and make a mess and let him "find" the hidden toys! My kids love this still, and they are 5 years old and 20 months old now.
Teach him baby sign language too. It is never to early to start. It will help him to learn to communicate, and is very helpful for them and us.
Teach him peek-a-boo games. Or, hide an object under a cup... then put nothing under another cup, and let him "pick" which one the object is "hiding" under. My daughter at this age, loved this game. She understood and found it fun. It teaches them skills & concepts at the same time.
Do shape sorters too. Sure, it's something that takes practice, but never underestimate them.... they will find it fun. They don't have to get it correct, but it's simply exposing them to "concepts." Give him stacking things too, show him how. In time, he will surprise and stack things too.
Introduce all kinds of things and concepts. Also give hima ball... roll it around. Babies love this too.
All the best, your'e doing great. No worries. Babies are entertained with anything...even if you put them down for a moment to wash the dishes, they are fine at knowing how to play. These are just some things I've done with my babies.
Good luck, hope this helps,