Factorise $8 x^{3}+27 y^{3}+36 x^{2} y+54 x y^{2}$

(A) The given expression is $8 x^{3}+27 y^{3}+36 x^{2} y+54 x y^{2}$.
We can rewrite this expression as:
$(2 x)^{3}+(3 y)^{3}+3(2 x)^{2}(3 y)+3(2 x)(3 y)^{2}$.
This is in the form of the algebraic identity $a^{3}+b^{3}+3 a^{2} b+3 a b^{2} = (a+b)^{3}$,where $a = 2 x$ and $b = 3 y$.
Substituting these values into the identity,we get:
$(2 x+3 y)^{3}$.
Thus,the factorised form is $(2 x+3 y)(2 x+3 y)(2 x+3 y)$.