let

r = the weight of a red cube

w = the weight of a white cube

b = the weight of a blue cube

3 red cubes and 1 white cube balance 3 blue cubes

3r + 1w = 3b

1 red cube and 3 blue cubes balance 3 white cubes

1r + 3b = 3w both sides add -3b

1r = 3w - 3b lets plug the value for r in 3r + 1w = 3b we get

3(3w - 3b) + w = 3b

9w - 9b + w = 3b

10w = 3b + 9b

10w = 12b divide both sides by 2

5w = 6b

6 blue cubes will balance 5 white cubes.