M  =  (1/6) {{-1, 3, -3, 1}, {3, -6, 3, 
              0}, {-3, 0, 3, 0}, {1, 4, 1, 
              0}};
Clear[u]; U = {u^3, u^2, u, 1};
B  =  {P1, P2, P3, P4};

MatrixForm[M]
MatrixForm[B]
MatrixForm[U]

P1 = {0, 0};
P2 = {1, 1};
P3 = {2, 0};
P4 = {3, 2};

For[u = 0; plist = {}, u ≤ 1.0, u = u + 0.05, 
      plist = Append[plist, U . M . B]]

plist

Graphics[{PointSize[0.025], Thickness[0.01], Line[plist], Point[P1], 
        Point[P2], Point[P3], Point[P4]}]

Show[%, Axes -> Automatic, 
      PlotRange -> {{0, 4}, {0, 3}}]