Well, עוגה is a feminine word, so you need היא. Usually, if a word ends with ה or ת, there is a high probability that it is feminine and other words are masculine. However, this is a rule with quite a few exceptions. You might want to check this post if you want to read more about it:
I have replayed this many times. I am hearing something like: "ugate ima"
Is pronounced: "ta'im"
Then why in the adjective describing something feminine (the cake) it takes the sound of "te'ima"...
What puzzles me is the vowel change from "ta" to "te"
Anyone has some insights?
The endings of the adjectives don't bother me as we have changes for adjectives in Spanish and German. I am familiar with the concept.
Since I have no idea why of this change, I will memorize the whole expression by heart, and see if this sound change is prevalent, and perhaps find a reason if there is any...
Yes, טעים is "ta'im" and טעימה is "te'ima". So עוגה טעימה is "ugá te'imá".
This vowel shift is actually very, very common with adjectives. The "e" sound here is actually a shva, which is sometimes pronounced and otherwise isn't. For example in the pair שמח "saméach" and שמחה "smechá", the shva under sin isn't pronounced. But for example "sweet" is מתוק "matók" and מתוקה "metuká" it is pronounced, just like טעימה. As you go down the tree, you will encounter many such adjectives.
Another note. If the "a" changes to shva in the feminine singular form, shva will remain in the plural forma as well. טעימים "te'imím" and טעימות "te'imót".
If you are not familiar with it, I recommend pealim.com as a wonderful tool that will help you with many pronunciation doubts you will have in the future.