"whatever we like" is correct and usable in written English.
You can use it to mean "anything that we choose". For example, "We can do whatever we like this weekend."
We just wear whatever we want, whatever we like.
We can do whatever we like with it, for as long as we live.
It's just the two of us, which allows the freedom to write about whatever we like.
We focus on hip-hop and indie genres and post reviews, downloads, videos, interviews and feature editorials on whatever we like!
God is telling them, they believe, that we humans are entitled to do whatever we like with the Earth and its resources.
"This comes from an entire culture that has been escalating toward an open and blunt language based on us being the chosen people who are allowed to do whatever we like".
We wandered into the restaurant kitchen to point at whatever we liked the look of.
"They'd stay open till 4am, playing Portishead, Sigur Rós, whatever we liked really, because we knew the owner".
It was a loose federation of graduate students and postdocs, and we could just do whatever we liked.
Richard had a university position, but the rest of us did not, and it was like a sort of a loose federation of graduate students and postdocs, and we could just do whatever we liked.
Although the epithet was originally rejected by the editors of Mycologia as "frivolous", Desjardin and colleagues insisted that "we could name it whatever we liked".
