what can i put instead of egg in cake?!

Buttermilk
Buttermilk is one of the preferred egg substitute used for eggless cake recipes. What you need to do is add half a cup of buttermilk (instead of one egg) and follow the same directions as you did for baking regular cakes. The only thing is to add less amount of water for making the dough. With buttermilk, the resultant cake will be very soft and tasty.

Pureed Fruits
So, you don't like using eggs and buttermilk in cakes? In such a case, a good egg substitute for baking cakes is, adding pureed fruits. Use 3 tablespoons of pureed banana (for one egg) and follow the same tips for baking cake. Even without eggs, you will surely serve a soft and delicious cake with pureed fruits.

Gelatin
Another popularly used egg substitute in baking is unsweetened and unflavored gelatin. Most vegetarians prefer adding this egg substitute in cake, instead of the other options. For using gelatin in baking cake, mix together one tablespoon gelatin with three tablespoons lukewarm water. Add this mixture for making the cake dough.

Flaxseed
You might have already heard about using flaxseed as an egg substitute in food recipes. For using flaxseed in baking an eggless cake, first combine one tablespoon of flaxseed oil with three tablespoons water (for using in place of one egg). Stir the mixture well and allow it to thicken for a few minutes. Strain the seeds by using a muslin cloth and use the filtrate for baking cake.

Vinegar and Baking Powder
Use this egg substitute in cake, only when you require more than one egg for baking. Mix one tablespoon each of white vinegar and water in a glass. To this, add one teaspoon of baking powder and stir well until the mixture blends well. Now, use this egg substitute for your cake recipe.

Eggs are what make a cake light and fluffy, You can use fruit purees but its going to change the flavor of the cake. I dont care what anyone else tells you. The honest to god best substitute for eggs in a cake is MAYO, but since you want egg free because of your diet, your best bet is to use 1 cup of apple sauce, or a banana in place of an egg. However, add another 1/2 tsp of baking soda to the mix to make the cake less dense as eggs also act as a leavening ingredient.

One thing I want people to remember if they ever see this question is baking is a science, more so than cooking, there is a reason for certain ingredients when it comes to baking and altering these ingredients no matter how slight is going to affect the profile and flavor of the item.

Im a chef.

1 tablespoon arrowroot powder + 1 tablespoon vegetable oil, mix together and then add 1/4 cup water.
You can also substitute cornstarch for the arrowroot powder but it is not quite as good.