I saw a picture of this square on Pinterest, it didn't have a pattern to go with it but I thought I'd give it a go anyway:
Rounds 1 and 2 are done in the same colour, following the granny square pattern (day 1), end off this colour and join in the second colour.
Round 3 - 3 double crochets in the corner space, 3 double crochets in the top of each treble crochet from round 2, in the chain space do 3 double treble crochets in the top of each treble crochet from round 1. Continue in this fashion all the way round, join the round with a slip stitch and end off this colour.
Round 4 - join in the next colour. In the corner double crochets do 2 triple crochets in the first stitch, triple crochet 1 chain triple crochet in the second stitch and 2 triple crochets in the third stitch. 2 chains, miss next 3 stitches, 3 treble crochets in the double treble stitches from round 3. Continue this pattern all the way round.
(As always this is in UK terms)
Repeat rounds 3 and 4 until the square is the size you want, ending with round 3. I have edged mine with a round of double crochets to finish it off.