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Speedo may be suffering from what is called "anaemia", a condition when there is a blood loss (i.e. from an ulcer or internal injury, fleas or other parasites) or the inability to produce red blood cells. A symptom of anaemia is exactly what Speedo is doing - licking concrete. Cat's may also eat kitty litter, become very weak or lethargic, along with pale gums.
This can be a serious condition therefore it is important to contact your vet to let him/her know of Speedo's new behavior.
Anemia is when the blood count is down. Your vet should be following your cats blood levels closely, but you should call and make sure. Anemia can be treated with medications to stimulate the bone marrow/ or transfusions...but to truly fix you need to find the cause.
I find that during medical treatment of certain diseases, they start this licking items behavior. I tell my clients to sprinkle small amounts of salt or salt substitue on the cats food and see if the behavior decreases..but talk with your vet as well.
You are welcome. Tell me how it goes!