Women are not easy to figure out, but let's start with the observation that when approached by males and other aliens, females—even those who never watched Star Trek—activate deflector shields. I'm not sure why this is; laboratory studies show that most females are quite attracted to males.
You can't penetrate this shield, you have to get them to lower it, and that's where your cube comes in. It's angular, it's masculine, it's mysterious; it makes you look resourceful, even playful. Often, that's intriguing enough to trigger a scan for intelligent life. To scan, many females use a technique known as flirting, and, like transporter beams, to flirt the deflector shield must be lowered.
To meet girls, take your cube to a female-rich environment and act natural. Maybe get a cup of coffee and read the paper. After a few minutes, pick up your cube and start solving.
Slowly. You're not going to impress with speed, so make it look hard. Ponder the cube intensely as if you were lost deep in concentration; brains are way cool. Line up the sides carefully so they turn smoothly and let your fingers do the talking.
Females within scanning range will be curious. A little drama helps, so don't rush things—let the tension build. The last move is perfect because the cube looks good and scrambled just before it all comes together.
When you're done, try to conceal the cube from optical sensors; one may plot an intercept course to get a closer look. Hail her.
Did she know that if there were a pair of shoes for every possible combination, each woman on the planet could change into a new pair 4 times a second for 100 years? And even that wouldn't be enough, would it?
If you get a smile, you're in. Be cool, but don't be timid. Boldly go where no man has gone before!