To learn bird songs you have to pursue the bird until you see it singing. Get it in your binoculars. Once you identify the bird you will know it's song wherever you go. In identifying them it's important to know what's in your region and habitat. Most people know more birds by sight and sound than they realize. It's fun to be able to ID birds by sound alone.
It's getting a little late for migrants so your bird is likely a local breeder. Xeno-canto is a good resource for recorded bird songs.
Here's some for the Hermit Thrush, a mountain bird closely related to American Robin, and one of the most beautiful, haunting songs in North America:
Hermit Thrush
Two other birds have melodious songs very similar to robin, the Black-headed Grosbeak and the Western Tanager:
Black-headed Grosbeak
Western Tanager