The phrase "are both cute and" is correct and usable in written English.
It can be used when describing two or more subjects that share a common quality, emphasizing that they possess that quality together.
Example: "The puppies are both cute and playful, making them irresistible to everyone who sees them."
Alternatives: "are equally adorable and" or "are charming and".
Snag a pair of the North Face's ETip gloves, which are both cute and functional, or pick up a set of Mountain Hardware's Power Stretch Stimulus Gloves, which make a nice grippy glove liner.
If you live in an urban area, their popularity seems to be growing, with new models (including an adorable convertible) that are both cute and classy.
David Norñoa ("Six Feet Under") manages to be both cute and deeply annoying as the office techno-nerd.
Robert Johnston, style director at GQ, put that success down to the fact it was both "cute" and "dead easy".
It's Roboquad, a cat-size robotic toy from WowWee (www.wowwee.com) that manages to be both cute and creepy at the same time.
The level in which you collect fluffy white Huffin Puffin chicks and turn them into temporary cotton trails is both cute and mechanically interesting, and (fabric spoiler alert) I'm surprised the developers waited until the final world to introduce velcro (alert ends).
They're basically inseparable, which is both cute and pretty intimidating when you think of the artistic powerhouse the two of them make.
By their own proclamation, they do "cool stuff that matters" and prefer not being evil, a claim validated when they rent goats instead of lawn mowers to trim weed at the Googleplex, in an activity they say is both "cute" and "low-carbon".
Nothing really beats a classic pencil skirt while a pleated skirt can be both cute and comfortable.
Foxes, as you would expect from the name, is both cute-looking and shrewd.
This is both really cute and really weird.
