Evaluate the following product without multiplying directly: $103 \times 107$

Without actually calculating the cubes,find the value of:
$\left(\frac{1}{2}\right)^{3}+\left(\frac{1}{3}\right)^{3}-\left(\frac{5}{6}\right)^{3}$

Expand $(4a - 2b - 3c)^2.$

Using a suitable identity,evaluate the following:
$103^{3}$

Factorise the expression: $\frac{4x^2}{9} - \frac{x}{3} + \frac{1}{16}$

Verify that $x^{3}+y^{3}+z^{3}-3xyz = \frac{1}{2}(x+y+z)[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}]$