I know of no Scriptural basis for Cherubs being baby Angels, or in fact that any Angels are infants. Additionally I find no reference to Cupid who is depicted as a infant with wings and bow and arrows anywhere in the Bible? If anyone is aware of any such Scriptures please inform me.
You are correct that the Bible does not consider angels to look like babies with wings. Angels sometimes appear in human form, or in some inexplicable and terrifying guise. Also, Cupid/Eros is part of classical mythology - and he is more typically an adolescent rather than a baby, though both images are possible. Generic "flying baby" images may represent nature spirits of some kind. This iconography was known to Renaissance artists via the survival of classical statuary, and adapted into Christian art. Its popularity at this time is largely due to the influence of Donatello, although there are many examples prior to him (Inventing the Renaissance Putto, Charles Dempsey, UNC Press 2001).
Properly speaking, the flying baby is a putto (plural putti). There are variants, like panisci who are the compatriots of the god Pan; spiritelli who are general nature spirits or fairies; and so on. They all generally play a supporting role, doing things like holding up garlands of flowers, playing miniature musical instruments, carrying important people on clouds, or just flitting around the edge of a painting; though there are also works where they are the subject. Important variants include the flying baby head (maybe with six wings, maybe with just two), and the cloudy/ghostly/translucent putto.
Here are a couple of examples of these. My first example is Madonna and Child with Seraphim and Cherubim by Andrea Mantegna, c. 1460. You can see that the background of the painting is entirely full of winged baby heads. They function here like an aureole (a sort of whole-body halo that surrounds particularly holy people); instead of abstract glowing rays, we have a mass of angels. Another incredibly famous example is the Sistine Madonna of Raphael, 1512. In an enlarged version of the image, it can be seen that the cloudy background is actually composed of angelic faces. The two putti at the bottom are more "conventional", and probably immediately recognizable. The background angels are part of the heavenly vision - transcendent and immaterial - while the foreground pair are a playful bridge between the painting-world and the exterior world. So in these examples, we see a spectrum of uses of the image, from alien to friendly.
Theologically - if there is any real theological justification behind artistic appropriation of classical myth - the portrayal of angels as children emphasizes their benevolence and innocence (ie, lack of sin). Simply put, they are meant to look cute. On the other hand, the flying heads are quite un-cute to my eyes: the adorable baby head is in an odd context, creating a striking dissonance which is suggestive of the sheer incomprehensibility of the Biblical angel, even if it's not a literal depiction. I'm thinking of the Ezekiel/Revelation kind of thing, which actually are cherubim, כְּרוּבִים. We can probably point to Donatello for the habit of showing angels as winged children, though to be fair his putti aren't as schmalzy as some more recent examples.
Dr. A Cohen, in his commentary on the Pentateuch explains the cherubim in Exodus 25: 18, as follows:
There is therefore a possibly very old tradition that link cherubim to children.