The shelf life of a cakesicle is 7-10 days if using fresh cake. Count the days based on when your cake was baked. If you use fresh frosting made with butter, you might want to consume them within 3-5 days.
Note: Mold will develop on the filling if you keep them longer than that and the problem is that you won't notice the mold until you bite into your cakesicle.
I know this from experience. Thankfully I cut into, instead of biting into, a 14-day-old cakesicle just to see what it looked like. When I saw the fuzzy white mold, I was so happy I used a knife instead of my teeth. Yuk!