To find out how many students suggested a rainbow-themed party, we can calculate 3/8 of the total number of students.
3/8 * 40 = <<3/8*40=15>>15
Therefore, 15 students suggested a rainbow-themed party.
To find out how many students did not suggest a rainbow-themed party, we can subtract the number of students who suggested a rainbow-themed party from the total number of students.
40 - 15 = <<40-15=25>>25
Therefore, 25 students did not suggest a rainbow-themed party. Answer: \boxed{15 \text{ suggested rainbow, 25 did not}}.