Gordon is correct, you will have to remove the version numbers from the Ensembl IDs before you can do anything with biomaRt. You should also note that the code you are using for biomaRt doesn't make any sense, as you are using code intended for a Bioconductor OrgDb package instead of actual code that will work for biomaRt. The correct call would be
> gns <- c("ENSMUSG00000102693.1", "ENSMUSG00000064842.1", "ENSMUSG00000051951.5","ENSMUSG00000102851.1", "ENSMUSG00000103377.1", "ENSMUSG00000104017.1")
> mart <- useMart("ensembl","mmusculus_gene_ensembl")
## try to map, including the version numbers
> getBM(c("ensembl_gene_id","entrezgene"), "ensembl_gene_id", gns, mart)
[1] ensembl_gene_id entrezgene
<0 rows> (or 0-length row.names)
## and now, after stripping them off
> getBM(c("ensembl_gene_id","entrezgene"), "ensembl_gene_id", gsub("\\.[1-9]$", "", gns), mart)
ensembl_gene_id entrezgene
1 ENSMUSG00000051951 497097
2 ENSMUSG00000064842 NA
3 ENSMUSG00000102693 NA
4 ENSMUSG00000102851 NA
5 ENSMUSG00000103377 NA
6 ENSMUSG00000104017 NA
As Gordon also noted, you should start out with the annotation service you want to use. There is no profit in trying to map from EBI/EMBL or GENCODE IDs to NCBI IDs, because there are any number of technical reasons that a particular ID might not map. For example, if we include the MGI symbols in our call to getBM, we can then use those to try to map Gene IDs to Ensembl Gene IDs
> z <- getBM(c("ensembl_gene_id","entrezgene","mgi_symbol"), "ensembl_gene_id", gsub("\\.[1-9]$", "", gns), mart)
> z
ensembl_gene_id entrezgene mgi_symbol
1 ENSMUSG00000051951 497097 Xkr4
2 ENSMUSG00000064842 NA Gm26206
3 ENSMUSG00000102693 NA 4933401J01Rik
4 ENSMUSG00000102851 NA Gm18956
5 ENSMUSG00000103377 NA Gm37180
6 ENSMUSG00000104017 NA Gm37363
> library(org.Mm.eg.db)
> select(org.Mm.eg.db, z[,3], c("ENTREZID","ENSEMBL"), "SYMBOL")
'select()' returned 1:1 mapping between keys and columns
SYMBOL ENTREZID ENSEMBL
1 Xkr4 497097 ENSMUSG00000051951
2 Gm26206 <NA> <NA>
3 4933401J01Rik 71042 <NA>
4 Gm18956 100418032 <NA>
5 Gm37180 <NA> <NA>
6 Gm37363 <NA> <NA>
So trying to map annotations between the different annotation services is difficult, because (for instance), all those Gm genes are predicted genes (predicted according to EBI/EMBL), but NCBI doesn't think they are a thing. And there are any number of NCBI predicted genes that don't have Ensembl IDs. Unless you care to know all the little technical details about what each service thinks is a gene, and where they differ, it's just best to pick on and stick with it.
This is a question about biomaRt so I have added biomaRt as a tag.
ok, thanks.