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\left(9t+4\right)\left(81t^{2}-36t+16\right)
Rewrite 729t^{3}+64 as \left(9t\right)^{3}+4^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right). Polynomial 81t^{2}-36t+16 is not factored since it does not have any rational roots.