The band "Apocalyptica" produces cello Rock Music, cello rock is a sub genre of rock music. They released the song "Bittersweet" on November 29 in 2004. (the question got the band confused with the song)
Grace - Apocalyptica song - was created in 2007.
Not Strong Enough - Apocalyptica song - was created on 2010-11-01.
Adam Gontier from Three Days Grace sang in the song I Don't Care by Apocalyptica.
Bittersweet - Fuel song - was created in 1998.
Heroes
Bittersweet - Miz song - was created on 2006-01-25.
Bittersweet - Hoodoo Gurus song - was created in 1985-06.
No, Three Days Grace and Apocalyptica are two different bands.However, the lead singer for Three days Grace, Adam Gontier, was featured in Apocalyptica's song I Don't Care.
Lacey Mosley from the band Flyleaf.
Bittersweet - Sophie Ellis-Bextor song - was created on 2010-05-02.
Apocalyptica was created in 1993.
The song you are talking about is probably the Toxicity version from the album "String Quartet Tribute to System of a Down" created by varius artists. Apocalyptica has nothing to do with either of the songs of that album.