I had this new blog in wordpress, and I am wondering why is it that some links (not mine of course) are being added to my content? Can this be due to my site was hacked or something else?

Quite possibly you are using a "sponsored" theme, where some company, usually in a highly competitive and spam filled marketplace have paid for the theme development and have it set to embed links in the content when certain words are used.

Are you talking about link in a footer or are they in the sidebar?

Are you able to remove them manually from an HTML code?

Are those links by chance encoded in base64? I believe there is an exploit in WordPress wp-register.php/wp-login.php that allowed someone to register and instantly have full admin access.

I had this issue with WP once, someone from China kept registering accounts on my blog via wp-register (WP settings to new registers was SUBSCRIBER, no admin access) and they were dumping base64 encoded javascript links into my HTML code templates that made links appear all over.