Are tones used in songs of Mandarin and Cantonese?

Both are tonal languages which means that the meaning of a single syllable/word depends on the pitch it is spoken with.

So, the answer is that even the linguists aren't sure about it. As San Duanmu states in "The Phonology of Standard Chinese" (ISBN 978-0-19-921578-2) there are two possible theories: a) either tones and musical notes are independently articulated or b) both are built by the same mechanism. Furthermore: "I believe that [...] tone and musical notes are made with the same articulatory mechanism and therefore they do interfere with each other. Unfortunately, I am not aware of any experimental study that demonstrates such interference (or the lack of it)" (Chapter 10, p. 252).

Fact is, Chinese speakers don't have problems perceiving the actual lyrics. Context does help where tonal information is missing. Furthermore it has been shown that song writers for Cantonese choose notes depending on the tones (Wong and Diehl).