Dear Student,
Yes. All the genes include all nucleotides of human DNA.
The stretch of DNA or RNA that codes for a Polypeptide (Proteins) are termed as Genes. Genes are inculcated in a segment of Chromosome. Chromosomes contains DNA that has nucleotide bases present in them. ( Adenine , Guanine , Cytosine , Thymine). Therefore every DNA has each nucleotide present in it , so does the Genes.
Proteins are a series of amino acids held together by peptide bonds. Each gene consists of nucleotide bound together which are elucidated by the cellular machinery in a group of THREE. These are called as Triplets. It is not necessary that every nucleotide in gene will code for an amino acid.
There are regulatory elements such as the Promoter of the gene which allows the enzyme to attach to the gene for the purpose of transcription. Similarly enhancers and Silencers can tune up or down transcription of a gene.
Regards