Good question. I'll answer it with scripture: After his resurrection, Jesus ate food in front of his Apostles in order to prove he was not a "ghost." The passage states:
"Why are you troubled? And why do questions arise in your hearts? Look at my hands and my feet, that it is I myself. Touch me and see, because a ghost does not have flesh and bones as you can see I have." And as he said this, he showed them his hands and his feet. While they were still incredulous for joy and were amazed, he asked them, "Have you anything here to eat?" They gave him a piece of baked fish; he took it and ate it in front of them (Luke 24:38-43).
In Acts 1:4 Jesus again appears to eat breakfast with the apostles. So the answer is, yes according to scripture God eats food.
Whether Jesus (God) has to eat out of necessity we don't know...probably not.
The answer is based on the assumption, you believe as most Christians do, that Jesus is the same God "from the beginning."
Hope this helps.