Led cube 4*4*4 with anodes horizontally
4 transistors 2N222 instead of BC337


The 2N2222 is 600 mA max and BC337 is 800 mA max.
Either will work fine, and with plenty of overhead. 




  Can you tell me, please, if I can use these components without
  recreate the Cube?


You do not need to make a cube out of the LEDs.
The 220 Ω resistors are what is recommended.