A double insulated cable is typically noticeable because when manufactured it will use material of two different colours. The wire will be surrounded by say in this example a red layer. They have a different colour over that like white so you can easily distinguish the inner protective layer for the one you'd see on the outside before cutting the cable open.

Many materials are made of two different types of plastics or rubber. Some so they are easily recognised, others easily read as the wire or cables will have been printed with information about its rating, use and sometimes even metre marks so you see the distance/length of cable each metre you pass over.

Some power cables have a softer exterior sheath which also has a lower melting point. This comes in very handy if your power system has been short-circuited but the consumption is less than your circuit breakers values. Over time the cable will heat up and if lucky/unlucky you'll notice the cable starting to smoulder or smell like it's burning. It's a clear sign something is not right, but if you're lucky the inner insulated layer will have a high melt point and it's still isolated protecting from catastrophic failure.

Sometimes the outer sheathing has a silicone based material so it slides easily against other rubbers. This type of material is commonly used where multiple cables need to be pulled through buildings during construction or in network cabinets where you might have hundreds of cables all in a small area.