To make a cake i need oil/olive oil right?

There is no such thing as 'baking oil' ... you can use any kind of vegetable oil, canola oil, or corn oil ... the stuff you fry things in is the same 'oil' you use in baking. DO NOT use 'extra virgin olive oil' to bake a cake ... that has a 'flavor' that might 'go away' when the oil is heated to baking temperatures, but it could leave an 'aftertaste' in your cake. If you don't have ANY oil, then use one egg and 1/2 cup of mayonnaise ... not 'salad cream' but any kind of 'plain' mayonnaise. There is a tiny bit of vinegar in the mayonnaise, but not enough to change the flavor much in your cake ... I actually make some cakes with mayonnaise instead of eggs and oil because I want that little 'twang' at the end of each taste that you can only get if you use mayonnaise.