Hi, first of all, you need to be very specific if you ask for classical music. "Songs" DO mean things meant to be sung.
Here's something that you might like since it combines classical with rock--Julian Lloyd Webber is cellist (the composer/arranger Andrew Lloyd Webber's brother).
https://www.youtube.com/watch?v=p1lpCszsOMU&ab_channel=AndrewLloydWebberMusicals
Below are other classical pieces featuring cello (that are more "straight classical")--these are fairly short pieces.
Bach Cello Suite No. 1--Prelude, cellist Yo-Yo Ma
https://www.youtube.com/watch?v=PCicM6i59_I&ab_channel=RaduR%C3%AEc%C4%83
The Swan -cellist Yo-Yo Ma
https://www.youtube.com/watch?v=zNbXuFBjncw&ab_channel=Nodame2006
"Jacqueline's Tears"--Jacqueline Du Pre
https://www.youtube.com/watch?v=1pmBJLI4kVw&ab_channel=biluka
This might be fun---here a young cellist playing with his university orchestra:
https://www.youtube.com/watch?v=breQHJnnSb8&ab_channel=hfmFRANZLISZTweimar