Rotating the cube by euler engles, carries the other axes together.

[Ketschak]

I am trying to use the signature: SetRotation(const Vector & axis, Real angle)

Could you help-me with it?

void App::ColorCubeLogic::OnProcessTick(const Logic::IState* state)
{
   static Double angleX = 0;
   static Double spinSpeed = 0.007;
   angleX += spinSpeed;
   angleX = Math::Fmod(angleX, Math::TWO_PI);
   
   Graph::Vector axis(Vector::ZERO_DIRECTION);
   axis.x = 1;
   axis.y = 1;
   axis.NormalizeAxisSelf();
   mCubeTransform->SetRotation(axis, angleX);

The vector axis defines the rotation axis (45° between x and y).
The vector needs to have unit length.
This can be accomplished with axis.NormalizeAxisSelf();