At the 2002 Winter Olympics in Salt Lake City, Kuske, along with teammates André Lange, Carsten Embach, Enrico Kühn, won the gold medal in the four-man event.

Four years later in Turin, Kuske paired with Lange to win the gold medal in the two-man event, while those two, along with teammates René Hoppe and Martin Putze, won gold in the four-man event.

Kuske won gold in the two-man and silver in the four-man event at the 2010 Winter Olympics in Vancouver.

With Florschütz, he competed at the 2014 Winter Olympics in Sochi in both the two-man and four-man event, but failed to win any medals.

After Florschütz and Arndt retired, Kuske joined the team of Nico Walther.