There are currently several songs titled 'Monster'.
So it'd probably be best so to Google a little of the song lyrics. If you try searching a particular lyric in quotation marks (for example "what's that coming over the hill") into Google, the search engines should recognize the lyrics and give you a bunch of possibilities.
Some bands that have released songs called Monster are:
Skillet (a Christian rock band) has a song called Monster.
Meg & Dia and contains the lyrics "His little whispers, love me, love me."
The Automatic and is more popular, containing the lyrics, "what's that coming over the hill? Is it a monster?".
There are also songs called Monster by Disturbed, Abandoned Pools and Lil Wayne.
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Green Day sings a song called warning
If you are referring to the Samsung with the Monster vs Aliens in it. The song is called Hey, Soul Sister by Train.
The song is called Sacrifice, by T.A.T.U.
Garth Brooks sings a beautiful song called "The River." Is he who you were thinking of? Delimomma
Firstly, the band is not monster mash, but its monster magnet, and the song is called "Live for the Moment"