Answer
$(2y+1)(4y^2-2y+1)$
Work Step by Step
The formula for factoring the sum of two cubes is: $A^3+B^3=(A+B)(A^2-AB+B^2)$.
The formula for factoring the difference of two cubes is: $A^3-B^3=(A-B)(A^2+AB+B^2)$.
Hence here: $8y^3+1=\\=(2y)^3+1^3\\=(2y+1)((2y)^2-2y\cdot1+1^2)\\=(2y+1)(4y^2-2y+1)$