What do you call the sponge part of a cake in Chinese?
If you are mentioning a cake that has no coating outside, it is called 蛋糕胚.
X胚 means an unfinished version of X. Such as 陶胚 is unfinished clay works.
Beause people think the finished cake should have the cream outside. The center part that does not have a coating is considered unfinished. So it is called 蛋糕胚。
Example:

[6寸基础戚风（蛋糕胚）](https://www.xiachufang.com/recipe/102208654/

Note: 戚风 is the name of style of the 蛋糕胚 in the link. There are also other styles.

If you are pointing at the &quot;bread&quot; part of a slice of cake, you can just call it 蛋糕 or 蛋糕的部分. Because that is a part that contains egg 蛋. For example,
我喜欢蛋糕的部分，很香。但是我不喜欢上面的奶油，太甜了。
I like the &quot;sponge part&quot;. it smells so good. 
But I don't like the cream on it. It is too sweet for me.