Answer
b[(a+2b)($a^{2}$ -2ab+4$b^{2}$)]
Work Step by Step
$a^{3}$b+8$b^{4}$=b($a^{3}$+8$b^{3}$ )=b[ $a^{3}$ +$(2b)^{3}$]=
b[(a+2b)($a^{2}$ -a2b+$(2b)^{2}$)]=
b[(a+2b)($a^{2}$ -2ab+4$b^{2}$)]
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