Direct numerical simulation of the flow in a lid-driven cubicalcavity has been carried out at high Reynolds numbers (based on the maximum velocity on the lid), between 12'000 and 22'000. An efficient Chebyshev spectral method has been implemented for the solution of the incompressible Navier-Stokes equations in a cubical domain. The Projection-Diffusion method \cite{kn:BAKHLA95,kn:LELA00,kn:LEPERLAB04} allows to decouple the velocity and pressure computation in very efficient way and the simple geometry allows to use the fast diagonalisation method for inverting the elliptic operators at a low computational cost. The resolution used up to 5.0 million Chebyshev collocation nodes, which enable the detailed representation of all dynamically significant scales of motion. The mean and root-mean-square velocity statistics are briefly presented.