Can we wrap a 1x1x1 cube with the blue 3x3 piece of paper, cutting along some edges without disconnecting it?

Here's a good puzzle that Clifford Pickover found at CTK Insights:

Is it possible to wrap the cube with a 3×3 piece of paper below it? Handling of the paper is subject to two conditions:

1. The paper may be only cut or folded along the crease lines.

2. The cutting should not cause pieces to separate.