Is it possible to build a hollow cube with the extra little cube being on top, in the middle of the 3x3x3 cube? (So that it looks like you took the middle little cube that can not be seen in the standard 3x3x3 configuration and put it on top, two layers higher.) /edit: You can ignore the pattern on the pieces.
Here is one solution, though I have paid no attention to the checkerboard colouring of the pieces in the picture.
R R V R V V T B B R A L T B T S B S A A L A S L T S LThis is diagrammed as the layers, where each piece is represented by a unique letter placed in each cube the piece occupies.