This page explains in detail the interactions between the Mario series and the Space Odyssey series.
The Super Mario Bros. Super Show! episode 9001: A Mario Odyssey
October 10, 1989

Mario and Luigi looking at HAL 9001.
The twenty-seventh live-action segment of the Mario TV show, broadcasted along the animated episode "On Her Majesty's Sewer Service", is a parody of 2001: a Space Odissey.
It's about Mario and Luigi having installed a super computer called HAL 9001 capable of making any kind of pizza they order. After a few tries, the computer starts operating against their orders and start making awful pizzas, finally even hypnotising the Mario Bros. In the end they're saved by the man that installed the computer, how deactivates it.
HAL 9001 and the way he escapes human control are obvious references to the computer HAL 9000 from 2001: A Space Odyssey, as well as the title of the episode being based on it.
The Super Mario Bros. Super Show! episode Star Koopa
November 29, 1989 MarioThe fifty-first episode of the Mario animated series is a parody of Star Wars and the Plumber's log at the beginning of the episode is number 2001, in reference to 2001: a Space Odyssey (see Mario X Star Wars#The Super Mario Bros. Super Show! episode Star Koopa for more).
The Super Mario Bros. Super Show! episode Robo Koopa
November 30, 1989 MarioThe fifty-second and last episode of the Mario animated series is a robotic-themed episode and like the previous episode fetures the Plumber's Log number 2001, in reference to 2001: a Space Odyssey.
License
DiC, that created the Mario TV show, holds no right over Arthur C. Clarke's Space Odissey series, in fact they only parodied it.