Just to add to what others have said. High blood glucose levels will definitely cause a greater need for water and much more urine output. Also many kitties when their glucose are high will pee outside of the box. The only other thing that could be a problem is if he has a UTI (urinary tract infection). If it is the high glucose levels causing the excess peeing and peeing outside the box, then your kitty is not being controlled well with the insulin.
If possible could you start home testing? That could help to tell whether the insulin you are using...I believe it is Vetsulin from reading your other posts..is working properly at the current dose. Also from your other posts it looks like you are using a prescription dry food. Dry foods, whether prescription or not tend to keep the glucose levels higher.
If you have any test results from the vet maybe you could post them along with some additional information, such as whether you are using Vetsulin, and what dose you started with and what dose you are currently at. All this data helps to put the "puzzle" together to get a clearer picture of what is happening.
BTW If you start home-testing it is MUCH cheaper than having to take your kitty to the vet for glucose curves or spot checks.