Yes you can. In fact several Italian cakes call for olive oil. If you substitue olive oil for vegetable oil in a recipe that doesn't call for it, you will probably notice a change in flavor and you may or may not like it.
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Yes, there are a number of substitution charts that you can find on the web that can tell you how much olive oil you need to replace the amount of butter in the cake. You can also find several olive oil cake recipes and I've used some Blood Orange Olive Oil to add a kick to chocolate cakes several times.