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Relevant wiki: Identical Objects into Identical Bins

There are a number of identities on the identical objects into identical bins page that can be used for this.

$p(30,3)=p(27,1)+p(27,2)+p(27,3)=1+13+p(27,3)=p(27,3)+14$

$p(27,3)=p(24,1)+p(24,2)+p(24,3)=1+12+p(24,3)=p(24,3)+13$

$p(24,3)=p(21,1)+p(21,2)+p(21,3)=1+10+p(21,3)=p(21,3)+11$

$p(21,3)=p(18,1)+p(18,2)+p(18,3)=1+9+p(18,3)=p(18,3)+10$

$p(18,3)=p(15,1)+p(15,2)+p(15,3)=1+7+p(15,3)=p(15,3)+8$

$p(15,3)=p(12,1)+p(12,2)+p(12,3)=1+6+p(12,3)=p(12,3)+7$

$p(12,3)=p(9,1)+p(9,2)+p(9,3)=1+4+p(9,3)=p(9,3)+5$

$p(9,3)=p(6,1)+p(6,2)+p(6,3)=1+3+3=7$

$p(12,3)=p(9,3)+5=7+5=12$

$p(15,3)=p(12,3)+7=12+7=19$

$p(18,3)=p(15,3)+8=19+8=27$

$p(21,3)=p(18,3)+10=27+10=37$

$p(24,3)=p(21,3)+11=37+11=48$

$p(27,3)=p(24,3)+13=48+13=61$

$p(30,3)=p(27,3)+14=61+14=75$

Thus, there are $\boxed{75}$ ways to distribute the 30 objects into the 3 boxes.