What is the boiling point and melting point of octane?

That depends on what kind of octane you are referring to. n-octane has much different melting and boiling points than iso-octane. Octane has 18 structural isomers. Assuming the person asking the question is interested in either n-octane or iso-octane:

n-octane

melting point: −57 °C, 216 K, -71 °F

boiling point: 125.52 °C, 399 K, 258 °F

iso-octane (also known as 2,2,4-Trimethylpentaneor isooctane)

melting point: -107.38 °C, 166 K, -161 °F

boiling point: 99.3 °C, 372 K, 211 °F