A cake is "a mixture of flour, eggs, sugar etc baked in the oven", or "some other food in a flat round shape". Whilst I guess the cheesecake fails the first test it would pass the second - having said that I don't suppose you would have any queries about a fishcake!!! I think your friend is probably stretching the interpretation of "cake" to satisfy her sweet tooth, but as giving things up for Lent is really a test of mental strength only she will know whether she has succeeded. I have given up chocolate, and last night my children melted chocolate to dip marshmallows in (children are cruel sometimes) - I was tempted to lick a spoon but decided if i did that I might as well go buy a family sized bar of dairy milk and eat the lot!