[math-fun] Base-10 cube-free Thue-Morse ?

Hello Math-Fun, is the Thue-Morse seq really cube-free? I mean, is it impossible to find any substring of 1's and 0's inside the T-M seq which would be a cube in base ten? Only the lone 1's are cubes ;-) ... I could not find any such substring using my pocket calculator... Perhaps in base 2? Best, E.