Random sets with three random numbers in it (sampling random points in a cube)

Each point inside a cube has three values (X, Y & Z axes). There are in-built functions in R, pertaining to the generation of sets with single random number (one number per observation), such as runif(), sample(), rnorm(), set.seed() etc. Thinking in a similar logic, the numbers are generated in a single axis, with those functions.

My question is:

• Is there any function to generate random sets with three random numbers in it (or generalising, random sets with more than one number per observation)?
• What should be the approach, if the answer is no for the former?